Completeness Theorems and the Separation of the First and Higher-Order Logic

2023-2024学年四川省成都市第七中学 (高新校区)高一上学期10月月考英语试题If you’re interested in pushing yourself academically while experiencing college life, our Summer Programs for Pre-College Students (SPP) can be ideal for you. In the programs, you will be able to make friends with fellow students, engage in social activities around the city and on campus, and experience pre-college summer study at one of the world’s top teaching and research universities.Our long-running summer term pre-college offerings include a choice of one-, two-, three-, and six-week programs that prepare you for success in college. With five exciting and challenging pre-college summer programs to choose from, you can earn college credit, discover a new subject area, perform cutting-edge research in university labs, or immerse yourself in hands-on learning.Academic lifeSPP invites you to join other highly motivated teens from 87 countries in our summer programs for high school students — and take the leap into college life and academics, which enables you to take on new academic challenges, explore a variety of interests and consider possible majors. You can take college courses alongside undergraduates either on campus or online. And you can also earn up to eight college credits by conducting in-depth STEM research with individual instructors or as part of a group project. Or, you can immerse yourself in a variety of stimulating noncredit seminars that blend lectures with experiential learning, discussions, and projects.Campus/Residence lifeEmbracing college life is an exciting experience. Whether you live on campus or commute, you’ll get to know the ins and outs of college and city life. If you live on campus, you will stay in the residence hall, sharing a room and participating in dorm activities. There are typically two students per room and safety is our highest priority: residence halls have live-in university staff and 24-hour security. Resident program assistants provide guidance, coordinate and lead social activities, ranging from group activities that include comedy shows to field trips.Your hard work will be combined with social events and fun activities —and you’ll still have time for your own adventures on campus! Email the SPP office at ******************.1. What does SPP aim to do?A．To help college students to achieve academic success.B．To provide admission guidelines for pre-college students.C．To get high school students well-prepared for college life.D．To encourage students to participate in hands-on learning.2. What are students supposed to do to earn the required credits?A．Carry out STEM research. B．Attend various seminars.C．Finish the courses online. D．Join in experiential learning.3. What can we know about students living on campus?A．They can organize social activities. B．They will have access to a single room.C．They are provided with good security. D．They are advised to direct comedy shows.“I can’t connect with your characters.”I kept hearing the same feedback and was unable to understand why and not sure what to do. I was a character-driven writer. How could I mess up the one thing I was supposed to be good at? I was determined to convince my agent that these characters were real. After all, I knew they were real. My main character Lotus had lived inside me for years. I just needed to clarify her on the page.I wrote and edited for a year, trying to respond to this agent’s feedback. But Lotus’ personality began to disappear. I tried to have her make “better” decisions, wear smarter fashion, and have more friends, as my agent said she acted “immature” and was “isolated”. And when this agent ultimately parted ways with me, I felt like I had failed. Now with time and distance, I realize I tried to fit Lotus into a neurotypical style to please my agent. And as a result, Lotus lost her Lotus-ness.When that agent discouraged me from writing Lotus as autistic(自闭的), he said that would make Lotus seem more “vulnerable(脆弱的)” or an “obvious victim”. I didn’t want Lotus to seem vulnerable. Lotus’ autism is what makes her powerful, I tried to explain. But from a neurotypical perspective, Lotus’ autism could only be seen as a weakness.Unsure of how to convince my agent of the strength and power autistic women hold, I began to write Lotus as “neurotypical”. And I failed miserably. After all, what do I know about being neurotypical? My whole life, autism was my default. Not being diagnosed until 2020, I assumed the way I saw the world was “normal”.My current agent encourages me to write from my neurodivergent(神经多样性的) experience. With this invitation, I revisited Lotus and saw her the way I first wrote her. And when I did, the characters and the entire narrative began to make more sense.Identifying my characters as neurodivergent not only gives me joy as a writer, but it has produced my strongest writing. For so long, I’ve combatted the advice to “write what I know”, in part because I didn’t know what I actually knew. I didn’t know I was neurodivergent. But a s I mine the specificity of my lived experience, my writing is stronger. There is a power to our lived experience. It’s not a limitation on our craft, but a swinging open of the gates.4. How did the author feel when receiving the repeated response from the first agent?A．Confused. B．Convinced. C．Determined. D．Disappointed. 5. Lotus’ personality got lost because ______A．Lotus no longer lived inside the author B．the author attempted to please the agent C．the agent failed to sympathize with Lotus D．Lotus was considered childish and lonely 6. What do we know about the author?A．She regretted parting with the agent.B．She owed her success in life to autism.C．She was aware of her autism in the early years.D．She was empowered by her autistic experience.7. What has the author learned from her own experience?A．Stick to your dream despite discouragement.B．Be true to yourself and write from your heart.C．Giving in to authority is the barrier to success.D．Everyone is born an original instead of a copy.At one time, the inheritance of traditional drama was difficult. People of insight screamed “save drama”. Many celebrities and big names put down their figures and went to the community to carry out public welfare performances of opera, and did everything possible to expand the coverage of drama. In recent years, traditional Chinese culture and art has gained a foothold on short video platforms and attracted a large number of young followers thanks to the explosive growth of the short video industry. Relaxing, emotional and fragmented, these video contents perfectly match the demands of the users. With the application of new technologies such as social communication and immersive experiencing, short video platforms are seeing more users, becoming a shining spot of new Internet media.Recently, Huangmei Opera “ Female Consort Prince ” became a hit on short video platforms as a lot of young users covered the aria (咏叹调) in their own way and showed great artistic talents. The interactive platforms are expanding the charm of the traditional opera among young people.Peking Opera was also well-received on short video platforms thanks to a series of augmented reality (AR) effects. Users love to film clips with a set of virtual facial makeup, headwear and costumes. Statistics indicate that these effects were applied by more than 18 million users, most of whom were young people.In addition to Chinese operas, intangible cultural heritage items, such as embroidery, paper-cutting, printing and dyeing, shadow play works, oiled paper umbrella making, and bamboo weaving are also actively promoted on short video platforms. In a word, short video platforms are becoming an important channel to display China’s intangible cultural heritage.Short video platforms, offering a fun, popular and easy way to explore the traditional art forms, are receiving a lot of positive feedbacks from China’s young generations. The seconds, or minutes long videos, along with unlimited possibilities as well as richness of styles, have produced remarkable achievements in promoting traditional Chinese culture.8. What mainly made the inheritance of traditional drama difficult?A．The slow growth of industry. B．The insufficient coverage of drama.C．The poorly-met demands of the users. D．The severe shortage of the drama actors.9. What led to the promotion of Peking Opera on short video platform?A．The social communication. B．The set of virtual facial makeup.C．The positive feedbacks from users. D．The application of new technologies.10. Why are paper-cutting and bamboo weaving mentioned?A．To expand the charm of traditional Chinese culture.B．To prove traditional art forms are actively promoted.C．To show the current situation of these cultural heritage.D．To offer new channels to display China’s cultural heritage.11. Which of the following is the best title for the text?A．The Bright Future of Huangmei Opera.B．The Explosive Growth of the Short Video Industry.C．The Simple Way to Explore the Traditional Art Form.D．The Creative Combination of Culture and Technologies.Several years ago, Jeremy Clarkson, presenter of the famous BBC television programme “Top Gear” discovered that one of his guests was half German and half Irish. Immediately, he said: “That's quite a strange combination. It's like, this must be done absolutely perfectly... tomorrow”.This joke played on stereotypes (刻板印象) of the Germans as efficient and the Irish as lazy. Many people could understandably be offended by these kinds of assertions (断言).We do not know every Irish person, so how can we then conclude that every Irish person is lazy?I recently read on a website that Irish business people were described as being 'generally rather casual' and more outwardly friendly than many European counties'. German business people, on the other hand, are considered to be very direct and according to the website, they do not need a personal relationship in order to do business. Once you hear advice like this,it becomes easier to understand where jokes like the one in the first paragraph come from.So why do some people disapprove of the kind of stereotypes as seen in Clarkson's joke, but not baring an eyelid (眨眼) when it comes to generalizations. What is the difference between the two?By definition, a stereotype is a widely held but fixed and oversimplified image or idea of a particular type of person or thing. A cultural characteristic, on the other hand, is a pattern of behaviour that is typical of a certain group.So what does this really mean? Stereotype are simply overstated assumptions about groups of people. Imagine if a tourist visited a small town in Switzerland and saw a number of locals playing the alphorn instrument, and then claimed that Swiss people can play the alphorn. This would be a stereotype! This is an overstated image of the Swiss which is based on one tourist's experience.If however, this tourist were to say that the Swiss are very punctual, this could be seen as a cultural characteristic. This is because it is a pattern of behaviour which is very typical in Switzerland: fromtheir transport system to their business meetings in this way, some people argue that generalizing another culture is not just useful. but important. Politicians always have to be mindful of the cultural characteristics of different countries. By becoming aware of different cultural characteristics,they can avoid causing offence (冒犯) in those cultures.However, others argue that generalizing cultures will always lead to offensive stereotypes. They argue that the best thing we can do is to stop generalizing cultures and start treating people as individuals.All this raises important questions: can making generalizations about groups of people be a positive thing? Or should we always avoid making broad assumptions about different groups?12. Whe n he said, “it's like, this must be done absolutely perfectly... tomorrow”，Jeremy Clarkson really meant________.A．the stereotypes of the Germans and the Irish are not so goodB．the combination of half German and half Irish is interestingC．the characteristics of the Germans and the Irish are oppositeD．the Germans will do it perfectly tomorrow while the Irish won't13. Which of the following is TRUE according to the passage?A．It's typical of the Swiss to be punctual.B．The Swiss can play the alphorn quite well.C．The Irish people are considered as lazy, direct and casual.D．The Germans are thought to be efficient, friendly and direct.14. Politicians think it important to generalize another culture because________.A．they don't want to offend other peopleB．generalizing will lead to offensive stereotypesC．cultural characteristics are better than stereotypesD．they think different cultural characteristics are useful15. The main purpose of this passage is to________.A．illustrate the importance of making generalizationsB．show it is wrong to play jokes on stereotypes of different peopleC．tell us the differences between stereotypes and cultural characteristicsD．discuss whether it is good to make generalizations about groups of people“Just think positively!”“It could be worse.”“You should look at the bright side!”We’ve all heard (and maybe used) these phrases without much thought. But they could be contributing to a culture of toxic(有毒的) positivity. For those new to this term, it might sound like an oxymoron(矛盾修辞法). How can positivity be toxic? Isn’t it supposed to be helpful, or “positive”, as the name suggests? 16“Toxic positivity is when somebody avoids all negative thoughts or feelings, pretending everything is going well when it is not,” explains Melissa Dowd, a therapist at PlushCare, a virtual health platform for primary care and mental health services.Whitney Goodman, the author of Toxic Positivity describes toxic positivity as the “endless pressure to be happy and pos itive, no matter what the circumstances are.” 17 It’s also something we can cause other people to experience. Expressing toxic positivity to others may look like offering them a simple solution to a complicated problem that we know nothing about, or not allowing people around you to appropriately express negative emotions.Toxic positivity causes us to suppress our emotions, which can make them worse. 18 “Although it can be helpful to look on the bright side when facing challenges,” Dowd says, “not copi ng with negative feelings in a healthy way in the moment can lead to those feelings resurfacing later in different areas of your life or as a form of anxiety.” 19 “If I feel like you’re going to dismiss me, I’m going to stop sharing how I’m feeling,” Goo dman adds.20 If you’re using toxic positivity against yourself, Goodman suggests remembering it’s OK if you’re upset about something. It’s valid if something annoys you. “Allow ourselves and other people to share when they’re going through a difficult time,” she says. Dowd adds that it’s essential that “we all learn to cope with and process our emotions in a healthy way as opposed to avoiding how we feel” as life’s stressors continue to rise. For example, instead of simply saying “Just think positively,”we’d better say “Sometimes bad things happen. How can I help?”This Too Shall PassWhen my family moved to Ohio over the summer, I feared attending another new school and knowing no one because I was able to expect what was coming. I had bright red hair and enormous glasses. In addition, I was_______and not very sociable.Boarding the school bus that first day, I felt like all eyes on me. I could hear the_______“She’s huge!” Obviously, the kids on the bus had known each other well. I spent that first bu s_______in silence.The following day was even_______. I did not notice that a few boys had tied a shoelace across the aisle and thus fell face first on the bus, _________everything I was carrying. _________I was embarrassingly gathering my supplies, I cou ld hear the laughter, and then the_______“That felt like an earthquake!” Anyway, I_______ to find a seat. Looking out of the window, I_______the tears welling up in my eyes.It was then that I sank into myself. I began walking everywhere. I would wander through the woods behind our house. I would also walk to a________about two miles down the road, where I would chat silently with myself. I began________the afternoon school bus on purpose, walking home instead. Then,________, I started losing weight. And as I became content with myself, I began making________.One of my newly-found friends also________with her weight, wanting to be a “perfect” cheerleader. She lived near my neighborhood so we would meet and________together. This became a daily activity with talking and laughing________the way—different from the lonely walks I had taken. My friend said that I didn’t have to be perfect. I just had to be me, and be happy with________. While I would not want to________that time of loneliness, sadness and embarrassment, Iam________I made it through. Whenever I am struggling with any other problem in life, I always remember the proverb “This too shall pass.” If you can find a path with no obstacles, it probably doesn’t________anywhere.21.A．outgoing B．overweight C．intelligent D．friendly22.A．whisper B．whistle C．giggle D．laugh23.A．drive B．lift C．ride D．travel24.A．worse B．longer C．funnier D．duller25.A．throwing B．losing C．leaving D．dropping26.A．Though B．While C．Since D．Because27.A．opinions B．statements C．comments D．discussions28.A．determined B．attempted C．pretended D．managed29.A．kept away B．took back C．put away D．held back30.A．garden B．market C．church D．library31.A．escaping B．missing C．delaying D．stopping32.A．uninterestedly B．uncertainly C．unfortunately D．unexpectedly 33.A．changes B．friends C．efforts D．decisions34.A．struggled B．competed C．dealt D．lived35.A．run B．play C．chat D．walk36.A．along B．across C．by D．in37.A．oneself B．myself C．herself D．itself38.A．relive B．remind C．relate D．rethink39.A．excited B．upset C．proud D．regretful40.A．exist B．stretch C．lead D．stay阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

高三英语阅读理解文章结构题单选题30题1.The author starts the passage with a question to _____.A.attract readers' attentionB.provide background informationC.introduce the main topicD.show the importance of the issue答案：A。

本题考查文章开头以问题开头的作用。

选项A，以问题开头通常是为了吸引读者的注意力，让读者产生好奇心从而继续阅读文章。

例如“Have you ever wondered why the sky is blue?”这样的问题会引发读者思考并想知道答案，进而继续阅读文章。

选项B，提供背景信息一般不是以问题开头的主要作用。

选项C，问题不一定直接引入主题，可能只是引起兴趣后再引入主题。

选项D，以问题开头不一定直接表明问题的重要性。

2.The first paragraph of the article begins with a story. This is to _____.A.make the article more interestingB.support the main argumentC.give an exampleD.provide historical context答案：A。

以故事开头通常是为了使文章更有趣，吸引读者。

比如以一个有趣的小故事开头，能让读者更容易投入到文章中。

选项B，故事开头不一定直接支持主要论点。

选项C，故事开头不一定是为了举例说明。

选项D，一般故事开头不是为了提供历史背景。

3.The article starts with a quote to _____.A.emphasize the author's pointB.show the author's knowledgeC.inspire readersD.provide an expert opinion答案：A。

不自满才能趋向完美英语作文英文回答：To strive for perfection, complacency must be eradicated. The pursuit of excellence necessitates an unwavering commitment to improvement and a constant drive to surpass one's own limitations.Complacency, an insidious foe of progress, lulls individuals into a state of contentment with their current abilities. It hinders growth and stifles the potential for greatness. When one becomes satisfied with what they have achieved, the desire to improve wanes, and the pursuit of perfection becomes an elusive goal.Uncompromising individuals, on the other hand, recognize that perfection is an ideal that can never be fully realized. Yet, they relentlessly strive to approach this unattainable horizon. They are driven by an unyielding belief that there is always room for improvement, and theyembrace challenges as opportunities for growth.Failure is not seen as a setback but rather as a stepping stone on the path to excellence. Mistakes become valuable lessons that inform their next endeavors. They are not afraid to venture outside their comfort zones, for itis in the realm of the unfamiliar that true progress is made.The pursuit of perfection requires a lifelong commitment to learning and self-reflection. Individuals must constantly seek out new knowledge and perspectives, and they must be willing to question their own assumptions. By embracing a growth mindset, they cultivate the capacity for continuous improvement.Moreover, perfectionism is not about attaining external validation or recognition. True perfection is internal, a reflection of one's own standards and values. It is a personal journey, a testament to the relentless pursuit of excellence.中文回答：不自满才能趋向完美。

2013年高考英语易错点点睛与高考突破专题14 阅读理解【2013高考预测】阅读理解是我们学习英语的主要目的之一，是我们获取外来信息的重要途径。

阅读理解是综合读者各方面知识的过程，通过阅读能看出作者的主要意图和文章的基调；从有关资料中汲取有用的东西；对不重要情节或信息一带而过；根据阅读目的和材料的难易程度调整阅读速度和方法；根据作者的描述得出自己的结论；掌握并利用语境猜测词的多种含义的；根据阅读材料快速读懂图表；根据短文的内容填空等等。

一、命题趋向1.阅读材料更趋向于真实性、实用性和教育性关注实际生活的选材特点在近年的NMET阅读理解试题中已经呈现出明显的增强趋势。

这种趋势与当前基础教育的改革要求是一致的。

中学生语言学习的根本目的应当与基础教育的根本目标一致，即:学会求知、学会做事、学会合作、学会做人。

真实性和适用性选材是适应基础教育英语课程改革的目标而出现的；选材的教育性是基于阅读的第二层面而设立的，即考生不仅要懂得文章的意思，还要进行思考。

2.问题的创设将会更加灵活多样，尤以整体理解和推理为主阅读理解创设的问题大多不能按字面意思随手拈来，需要归纳、概括中心，推测作者意图、挖掘深层含义。

有些题目还要加以逻辑推理才能选择出正确答案。

3.由猜测词义到对整个句子意义的理解将是一个新的命题热点词义猜测题在近几年的阅读命题中屡见不鲜。

一般是利用上下文，通过对应结构或平行结构中同义词或反义词来进行判断。

近年来考试突破了这个圈圈，命题者要求考生在对文章的整体理解上来理解某个熟悉的词汇或短语在真实语境中新的含义。

4.所选材料的结构复杂化，生疏但能读懂的短语和表达方式将达到一定的数量英语新课程标准中，阅读理解的要求更高。

在典型例题卷的阅读理解中就出现了许多考生感到陌生的短语。

如B篇中有to look the otherway；E篇中的in the great majority of等。

这些短语的出现在一定的程度上加大了难度，但符合《考试说明》的要求，也体现了语言学习的适用性和灵活性。

高一英语哲学观点单选题40题1. “The unexamined life is not worth living.” This quote is attributed to which ancient philosopher?A. PlatoB. AristotleC. SocratesD. Pythagoras答案：C。

Socrates 以“未经审视的生活不值得过”这句名言而闻名。

Plato 是苏格拉底的学生，主要作品有《 理想国》等；Aristotle 是柏拉图的学生，是一位伟大的哲学家和科学家；Pythagoras 以毕达哥拉斯定理等成就闻名。

2. Which philosopher is known for his concept of the “Categorical Imperative”?A. Immanuel KantB. Friedrich NietzscheC. René DescartesD. John Locke答案：A。

Immanuel Kant 提出了“绝对命令”（Categorical Imperative）的概念。

Friedrich Nietzsche 以批判传统道德和提出超人哲学等闻名；René Descartes 以“我思故我在”等观点著名；John Locke 主要在政治哲学和认识论方面有重要贡献。

3. “To be is to be perceived.” This statement is associated with whichphilosopher?A. George BerkeleyB. David HumeC. Thomas HobbesD. Adam Smith答案：A。

George Berkeley 提出“存在就是被感知”。

David Hume 是经验主义哲学家；Thomas Hobbes 在政治哲学方面有重要贡献；Adam Smith 是经济学家。

了不起的盖茨比第七章英语单词知乎以下是《了不起的盖茨比》第七章中出现的一些单词及其用法解释：1. Debauch: (verb) to corrupt morally or by intemperance or sensuality.Example: The wild party in Gatsby's mansion was filled with debauchery and excess.2. Sotto voce: (adverb) in a low voice, or in an undertone.Example: Jordan spoke to Nick sotto voce, revealing a secret that nobody else could hear.3. Affront: (verb) to insult intentionally.Example: Tom felt affronted when Gatsby openly declared his love for Daisy.4. Elude: (verb) to evade or escape from, as by daring, cleverness, or skill.Example: Despite all efforts, the truth about Gatsby's past eluded everyone.5. Nebulous: (adjective) hazy, vague, indistinct, or confused.Example: Gatsby's actual identity remained nebulous to many of his party guests.6. Meretricious: (adjective) alluring by a show of flashy or vulgar attractions, but often without real value.Example: Daisy was not impressed by the meretricious displays of wealth at Gatsby's parties.7. Contemptuous: (adjective) showing or expressing contempt or disdain; scornful.Example: Tom looked at Gatsby with a contemptuous expression, as he considered him a social climber.8. Ineffable: (adjective) incapable of being expressed or described in words; inexpressible.Example: Daisy experienced an ineffable sense of longing when Gatsby took her for a drive in his fancy car.9. Ramification: (noun) a consequence or implication; a branching out.Example: The ramification of Gatsby's obsession with Daisy was the destruction of his own life.10. Libertine: (noun) a person who is morally or sexually unrestrained, especially a dissolute man.Example: Gatsby was often seen as a libertine, indulging in extravagant parties and relationships.11. Sluggish: (adjective) displaying slow or lazy movements or responses.Example: The sluggish summer heat made everyone at the party feel lethargic and unmotivated.12. Pander: (verb) to cater to the lower tastes or base desires of others.Example: Gatsby's extravagant parties were seen by some as an attempt to pander to the desires of the wealthy elite.13. Incarnation: (noun) a particular physical form or state; a concrete or actual form of a quality or concept.Example: Gatsby believed that he could recreate himself into an incarnation of the man Daisy truly desired.14. Inexplicable: (adjective) unable to be explained or accounted for.Example: Daisy's sudden attraction towards Gatsby seemed inexplicable to many, considering their past.15. Insidious: (adjective) proceeding in a gradual, subtle way, but with harmful effects.Example: Tom warned Daisy about Gatsby's insidious intentions, accusing him of trying to steal her away.16. Supercilious: (adjective) behaving or looking as though one thinks they are superior to others; arrogant.Example: Tom's supercilious attitude towards Gatsby was evident in his condescending mannerisms.17. Saunter: (verb) to walk in a slow, relaxed, and confident manner.Example: Gatsby sauntered across the lawn towards Daisy, trying to appear nonchalant.18. Harrowed: (adjective) distressed or disturbed.Example: Gatsby's harrowed expression revealed the emotional turmoil he was experiencing.19. Truculent: (adjective) eager or quick to argue or fight; aggressively defiant.Example: Tom showed his truculent nature when he confronted Gatsby about his relationship with Daisy.20. Portentous: (adjective) of or like a portent; foreboding; full of unspecified meaning.Example: The dark clouds and thunderous sky seemed portentous, as if something significant was about to happen.21. Gaudiness: (noun) the quality of being tastelessly showy or overly ornate.Example: Despite the gaudiness of Gatsby's mansion, the guests were drawn to its opulence.22. Indiscernible: (adjective) impossible to see or clearly distinguish.Example: In the chaos of the party, individual voices became indiscernible and blended into a cacophony.23. Intermittent: (adjective) occurring at irregular intervals; not continuous or steady.Example: The intermittent rain throughout the night dampened the enthusiasm of the party guests.24. Stratum: (noun) a layer or a series of layers of rock in the ground.Example: Gatsby tried to climb the social stratum, hoping to be accepted by the upper class.25. Harlequin: (noun) a character in traditional pantomime; a buffoon.Example: Gatsby's harlequin smile hid the sadness and longing he felt for Daisy.26. Disconcerting: (adjective) causing one to feel unsettled or disturbed.Example: Daisy's disconcerting confession about her true feelings left Gatsby feeling disoriented and hurt.请注意，以上的双语例句是根据所给的单词和上下文进行编写的，但并非《了不起的盖茨比》中的原文。

Justice is a fundamental concept in society,embodying the principles of fairness, impartiality,and equity.It ensures that every individual is treated equally under the law and that their rights are protected.The pursuit of justice is essential for maintaining social order and fostering a sense of trust among citizens.In an essay on justice and fairness,one might begin by discussing the importance of justice in a democratic society.Democracy thrives on the belief that every citizen has an equal voice and that their rights are safeguarded.Justice is the cornerstone of this belief, ensuring that the law is applied fairly to all individuals,regardless of their social status, wealth,or influence.The essay could then delve into the various aspects of justice,such as distributive justice, which focuses on the fair distribution of resources and opportunities among members of society.This aspect of justice is crucial in reducing inequality and ensuring that everyone has a fair chance to succeed.Procedural justice is another important aspect that the essay could explore.It refers to the fairness of the processes and procedures used in decisionmaking and dispute resolution.A fair process is one that is transparent,consistent,and unbiased,allowing every individual to have their grievances heard and addressed.The essay might also discuss the challenges to achieving justice and fairness in todays world.Factors such as corruption,discrimination,and social biases can hinder the pursuit of justice.It is essential to address these issues through strong legal frameworks, education,and public awareness campaigns to promote a culture of fairness and equality.Moreover,the essay could highlight the role of institutions in upholding justice.Courts, law enforcement agencies,and regulatory bodies play a critical role in ensuring that justice is served.They must operate with integrity and impartiality to maintain public trust and uphold the rule of law.In conclusion,the essay would emphasize the importance of justice and fairness in building a just society.It would call for collective efforts from individuals,institutions, and governments to promote and protect these values.By doing so,we can create a society where everyone is treated with dignity and respect,and their rights are protected, regardless of their background or circumstances.。

Appears in Proceedings of17th Int’l Joint Conference on Artificial Intelligence(IJCAI’01).Theorem Proving with Structured TheoriesSheila McIlraith and Eyal AmirDepartment of Computer Science,Gates Building,Wing2AStanford University,Stanford,CA94305-9020,USAsheila.mcilraith,eyal.amir@AbstractMotivated by the problem of query answering overmultiple structured commonsense theories,we ex-ploit graph-based techniques to improve the ef-ficiency of theorem proving for structured theo-ries.Theories are organized into subtheories thatare minimally connected by the literals they share.We present message-passing algorithms that reasonover these theories using consequencefinding,spe-cializing our algorithms for the case offirst-orderresolution,and for batch and concurrent theoremproving.We provide an algorithm that restricts theinteraction between subtheories by exploiting thepolarity of literals.We attempt to minimize thereasoning within each individual partition by ex-ploiting existing algorithms for focused incremen-tal and general consequencefinding.Finally,wepropose an algorithm that compiles each subtheoryinto one in a reduced sublanguage.We have proventhe soundness and completeness of all of these al-gorithms.1IntroductionTheorem provers are becoming increasingly prevalent asquery-answering machinery for reasoning over single or mul-tiple large commonsense knowledge bases(KBs)[3].Com-monsense KBs,as exemplified by Cycorp’s Cyc and the HighPerformance Knowledge Base(HPKB)systems developed byStanford’s Knowledge Systems Lab and by SRI often com-prise tens/hundreds of thousands of logical axioms,embody-ing loosely coupled content in a variety of different subjectdomains.Unlike mathematical theories(the original domainof automated theorem provers),commonsense theories are of-ten highly structured and with large signatures,lending them-selves to graph-based techniques for improving the efficiencyof reasoning.Graph-based algorithms are commonly used as a meansof exploiting structure to improve the efficiency of reason-ing in Bayes Nets(e.g.,[18]),Constraint Satisfaction Prob-also provide an algorithm for compiling partitioned proposi-tional theories into theories in a reduced sublanguage.Wehave proven the soundness and completeness of all of thesealgorithms with respect to reasoning procedures that are com-plete for consequencefinding in a specified sublanguage.Proofs omitted from this paper can be found at[22].2Partition-Based Logical ReasoningIn this section we describe the basic framework adopted inthis paper.We extend it with new soundness and complete-ness results that will enable us to minimize local inference.Following[3],we say that is a partitioning ofa logical theory if.Each individual isa set of axioms called a partition,is its signature(the set of non-logical symbols),and is its language(the set of formulae built with).The partitions mayshare literals and axioms.A partitioning of a theory in-duces a graphical representation,,which wecall the theory’s intersection graph.Each node of the in-tersection graph,,represents an individual partition,,(),two nodes are linked by an edge ifand have a non-logical symbol in common(),and the edges arelabeled with the set of symbols that the associated partitionsshare().We refer to as thecommunication language between partitions and.Weensure that the intersection graph is connected by adding aminimal number of edges to with empty labels,.Figure1illustrates a propositional theory in clausal form(left-hand side)and its partitioning displayed as an intersec-tion graph(right-hand side).(Figures1,2and3first appearedin[3].)a Derive a subsuming formula or initially add to andderive inconsistency.Figure2:A forward message-passing algorithm.Figure3illustrates an execution of the FMP algorithm us-ing resolution as the consequencefinder within a partition.As can be seen from the example,the partitioning reduces thenumber of possible inference steps by precluding the directresolution of axioms residing in different partitions.Indeed,[3]showed that partition-based reasoning reduces the searchspace significantly,as a function of the size of the communi-cation language between partitions.FMP is sound and complete if we guarantee some proper-ties of the graph and the consequencefinders used for eachpartition.The graph is required to be a tree that is properlylabeled for.Definition2.2(Proper Labeling)A tree-structured repre-sentation,,of a partitioned theoryis said to have a proper labeling,if for alland,the two subtheories of on the two sides of theedge in,it is true that.Using FMP to prove(m1)(m5) (m5)(m6)clause passed from to(9)(m8) (m8)from in Figure1after asserting(13),2For clausal theories,we say that clause subsumes if there is a substitution such that.Observe that every reasoner that is complete for-consequencefinding is also complete for-generation,forany language that is closed under subsumption[14].The notion of a consequencefinder restricting consequence gen-eration to consequences in a designated sublanguage wasdiscussed by Inoue[17],and further developed by del Val [14]and others.Most results on the completeness of con-sequencefinding exploit resolution-based reasoners,wherecompleteness results for-consequencefinding are gener-ally restricted to a clausal language.The FMP reasoners in Theorem2.4must be complete for-generation in arbi-trary FOL languages,.Corollary2.6refines Theorem2.4 by restricting and to propositional clausal languages and requiring reasoners to be complete for-consequence finding rather than-generation.Corollary2.6(Soundness and Completeness)Let be a partitioned theory of propositional clauses,a tree that is properly labeled with respect to,and, ,a query.Let for such thatand(there is only one such),and let be reasoning procedures associated with partitions.If every is complete for-consequencefinding theniff FMP(,,)outputs YES.In Section5we provide examples of reasoners that are complete for-consequencefinding and show how to exploit them to focus reasoning within a partition.3Local Inference Using ResolutionIn this section,we specialize FMP to resolution-based con-sequencefinders.Resolution[26]is one of the most widely used reasoning methods for automated deduction,and more specifically for consequencefinding.It requires the input for-mula to be in clausal form,i.e.,a conjunction of disjunctions of unquantified literals.The resolution rule is complete for consequencefinding(e.g.,[19;27])and so is linear resolu-tion and some of its variants(e.g.,[23]).We present algorithm RESOLUTION-M-P(RES-MP),that uses resolution(or resolution strategies),in Figure4. The rest of this section is devoted to explaining four differ-ent implementations for subroutine RES-SEND(,,),used by this procedure to send appropriate messages between par-titions:thefirst implementation is for clausal propositional theories;the second is for clausal FOL theories,with associ-ated graph,that is a properly labeled trees and whose labels include all the function and constant symbols of the language; the third is also for clausal FOL theories,however it uses un-skolemization and subsequent Skolemization to generate the messages to be passed between partitions;the fourth is a re-finement of the third for the same class of theories that avoids unskolemization.In the propositional case,subroutine RES-SEND(,,) (Implementation1)simply adds to,as done in FMP. If the resolution strategies being employed satisfy the condi-tions of Corollary2.6,then RES-MP is sound and complete. In the FOL case,implementing RES-SEND requires more care.To illustrate,consider the case where resolution gener-ates the clause(a constant symbol and a vari-able).It also implicitly proves that.RES-MPPROCEDURE RESOLUTION-M-P(RES-MP)(,,)a partitioned theory,a graph,a queryformula in the language of().1.Determine as in Definition2.1.2.Add the clausal form of to.3.Concurrently,(a)Perform resolution for each of the partitions,.(b)For every such that,if partitionincludes the clause(as input or resolvent)and thepredicates of are in,then perform RES-SEND(,,).(c)If is proven in,return YES.Figure4:A resolution forward message-passing algorithm. may need to send from one partition to another, but it cannot send if is not in the communicationlanguage between partitions(for ground theories there is no such problem(see[27])).In thefirst-order case,complete-ness for consequencefinding for a clausalfirst-order logiclanguage(e.g.,Lee’s result for resolution)does not guaran-tee completeness for-generation for the corresponding full FOL language,.This problem is also reflected in a slightlydifferent statement of Craig’s interpolation theorem[10]that applies for resolution[27].A simple way of addressing this problem is to add all con-stant and function symbols to the communication language between every connected set of partitions.This has the advan-tage of preserving soundness and completeness,and is sim-ple to implement.In this case,subroutine RES-SEND(,, )(Implementation2)simply adds to,as done in FMP. In large systems that consist of many partitions,the addi-tion of so many constant and function symbols to each of the other partitions has the potential to be computationally inef-ficient,leading to many unnecessary and irrelevant deduction steps.Arguably,a more compelling way of addressing the problems associated with resolution forfirst-order theories is to infer the existential formula from,send this formula to the proper partition and Skolemize it there. For example,if is the clause that RES-SEND gets,replacing it with eliminates unneces-sary work of the receiving partition.The process of conservatively replacing function and con-stant symbols by existentially quantified variables is called unskolemization or reverse Skolemization and is discussed in [5;9;8].[8]presents an algorithm U that is complete for our purposes and generalizes and simplifies an algorithm of[9]. (Space precludes inclusion of the algorithm.)Theorem3.1([8])Let be a vocabulary and be for-mulae such that and.There exists that is generated by algorithm U such that. Thus,for every resolution strategy that is complete for-consequencefinding,unskolemizing using procedure U for and then Skolemizing the result gives us a com-bined procedure for message generation that is complete for -generation.This procedure can then be used readily in RES-MP(or in FMP),upholding the soundness and com-pleteness to that supplied by Theorem2.4.The subroutine RES-SEND(,,)that implements this approach is pre-sented in Figure5.It replaces with a a set of formulae in that follows from.It then Skolemizes the re-sulting formulae for inclusion in.PROCEDURE RES-SEND(,,)(Implementation3)a formula,.1.Unskolemize into a set of formulae,in,treat-ing every symbol of as a Skolem symbol. 2.For every,if is not subsumed by a clause that isin,then add the Skolemized version of to the set ofaxioms of.Figure5:Subroutine RES-SEND using unskolemization.Procedure U may generate more than one formula for any given clause.For example,if,for,then we must gener-ate both and(entails both quantified formulae,and there is no one quan-tified formula that entails both of them).In our case we can avoid some of these quantified formulae by replacing the un-skolemize and then Skolemize process of RES-SEND(Imple-mentation3)with a procedure that produces a set of formulae directly(Implementation4).It is presented in Figure6.PROCEDURE RES-SEND(,,)(Implementation4)a formula,.1.Set.2.For every term instance,,in,if andis not a subexpression of another termof with,then replace with“”for some newvariable,(if,is a constant symbol).3.Nondeterministically a,for every pair of marked arguments“”,“”,in,if are unifiable,then unify alloccurrences of(i.e.,unify for all markings,).4.For every marked argument“”in,do(a)Collect all marked arguments with the same variable onthe left-hand side of the“”sign.Suppose these are.(b)Let be all the variables occurring in.For every,replace“”within,for a fresh function symbol(if,is a fresh constant symbol).5.Add to.in[8],simplifying where appropriate for our setup.Our procedure differs from unskolemizing procedures in step4, where it stops short of replacing the Skolem functions and constants with new existentially quantified variables.Instead, it replaces them with new functions and constant symbols. The nondeterminism of step3is used to add all the possible combinations of unified terms,which is required to ensure completeness.For example,if and,then RES-SEND adds to,for a new constant symbol,.If,for ,then RES-SEND addsto,for new function symbols.Finally,if,then RES-SEND addsand to,for new function symbols.Theorem3.2(Soundness&Completeness of RES-MP) Let be the partitioned theory of propositional orfirst-order clauses,a tree that is properly labeled with respect to,and,a sentence that is the query.iff applying RES-MP(,,)(with Implementation4of RES-SEND)outputs YES.P ROOF SKETCH Soundness and completeness of the algo-rithm follow from that of FMP,if we show that RES-SEND (Implementation4)adds enough sentences(implying com-pleteness)to that are implied by(thus sound)in the restricted language.If we add all sentences that are submitted to RES-SEND to without any translation,then our soundness and com-pleteness result for FMP applies(this is the case where we add all the constant and function symbols to all).We use Theorem3.1to prove that we add enough sentences to.Let be a quantified formula that is the result of ap-plying algorithm U to.Then,results from a clause generated in step4of algorithm U(respectively,Step3in RES-SEND).In algorithm U,for each variable,the mark-ings“”in are converted to a new variable that is existentially quantified immediately to the right of the quan-tification of the variables.is a result of ordering the quantifiers in a consistent manner to this rule(this process is done in steps5–6of algorithm U).Step4of RES-SEND performs the same kind of replace-ment that algorithm U performs,but uses new function sym-bols instead of new quantified variables.Since each new quantified variable in is to the right of the variables on which it depends,and our new function uses exactly those variables as arguments,then Step4generates a clause from that entails.Thus,the clauses added to by RES-SEND entail all the clauses generated by unskolemiz-ing using U.From Theorem3.1,these clauses entail all the sentences in that are implied by.To see that the result is still sound,notice that the set of clauses that we add to has the same consequences as in(i.e.,if we add those clauses to we get a conser-vative extension of).PROCEDURE POLARIZE(,,)a partitioning of the theory,a tree anda query formula in().1.For every,set to be the set of object andfunction symbols that appear in,if there are any.2.Rewrite such that all negations appear in front ofliterals(i.e.,in negation normal form).3.Determine as in Definition2.1.4.For all such that,for every predicate symbol,(a)Let be the two sets of vertices in separated byin,with.(b)If appears in then,if appears in or appears in,forsome,then add to.5.Return.Figure7:Constraining the communication language of by exploiting polarity.our method is useful in cases where symbols appear with dif-ferent polarities in different partitions.5Minimizing Local InferenceTo maximize the effectiveness of structure-based theorem proving,we must minimize local inference within each node of our tree-structured problem representation,while preserv-ing global soundness and completeness.First-order and propositional consequencefinding algorithms have been de-veloped that limit deduction steps to those leading to interest-ing consequences,skipping deduction steps that do not.In the propositional case,the most popular algorithms are certain-(prime)implicatefinders.(See[21]for an excellent survey.)SOL-resolution(skipping ordered linear resolution) [17]and SFK-resolution(skip-filtered,kernel resolution)[14] are twofirst-order resolution-based-consequencefinders. SFK-resolution is complete forfirst-order-consequence finding,reducing to Directional Resolution in the proposi-tional case[13].In contrast,SOL-resolution is not complete forfirst-order-consequencefinding,but is complete for first-order incremental-consequencefinding.Given new in-put,an incremental-consequencefinderfinds the conse-quences of that were not entailed by alone.Defining completeness for incremental-consequencefinding is anal-ogous to Definition2.5.In the rest of this section,we propose strategies that exploit our graphical models and specialized consequencefinding al-gorithms to improve the efficiency of reasoning.Following the results in previous sections,using SFK-resolution as a rea-soner within partitions will preserve the soundness and com-pleteness of the global problem while significantly reducing the number of inference steps.SFK-resolution can be used by all of the procedures below.Unless otherwise noted,the algorithms we describe are limited to propositional theories becausefirst-order consequencefinders may fail to terminate, even for decidable cases of FOL.Thefirst strategy is compilation.Figure8provides an al-gorithm,COMPILE(,),that takes as input a parti-tioned theory and associated tree,that is properly labeled,and outputs a compiled partitioned theory.Each new partition is composed of the logical consequences of partition that are in the language,all the com-munication languages associated with.Prime implicatefinders have commonly been used for knowledge compila-tion,particularly in propositional cases.SFK-resolution can be used as the sound and complete-consequencefinder inStep2of COMPILE.Knowledge compilation can often create a large theory. Each partition produced by COMPILE(,)will be of worst case size of clauses.Since our as-sumption is that partitions are produced to minimize commu-nication between partitions,should be much smaller than.As a consequence,we might expect the compiled theory to be smaller than the original theory, though this is not guaranteed.Under the further assumption that the theories in partitions are fairly static,the cost of com-pilation will be amortized over many queries.We discuss further options for compilation,including the use of partial compilation,in a longer paper.PROCEDURE COMPILE(,)a partitioning of the theory,a tree with proper labeling for.For each partition,For,1.Leting a sound and complete-consequencefinder,perform-consequencefinding on each partition,placing the output in a new partition.Figure8:A partition-based theory compilation algorithm.Proposition5.1Let be a partitioned theory with associated tree that is properly labeled for.Let).For all,iff,where are the compiled partitions output by COMPILE(,).We may use our compiled theories in several different strategies for batch-style and concurrent theorem proving,as well as in our previous message-passing algorithms.Figure 9presents an algorithm for batch-style structure-based the-orem proving.BATCH-MP takes as input a(possibly com-piled)partitioned theory,associated tree that is properly labeled,and query.For each partition in order,it exploits focused-consequencefinding to compute all the relevant consequences of that theory.It passes the conclusions to-wards the partition with the query.This algorithm is very sim-ilar to the bucket elimination algorithm of[13].BATCH-MP preserves soundness and completeness of the global problem, while exploiting focused search within each partition. Theorem5.2(Soundness and Completeness)Let be a set of clauses in propositional logic.Let be the -consequencefinders associated with partitionsPROCEDURE BATCH-MP(,,)a(compiled)partitioning of the theory,a properly labeled tree describing the connections between the par-titions,a query in().1.If,is a compiled theory,replace partition withthe partition from the uncompiled theory.2.Determine as in Definition2.1.3.Let for such that and a.4.Following in a decreasing order,for every suchthat,Run the-consequencefinder on until it has exhaustedits consequences,and add the consequences in to.5.If is proven b in,return YES.a There is only one such.b Derive a subsuming formula or initially add to andderive inconsistency.Figure10:A concurrent message-passing algorithm.reason with logical rather than probabilistic theories,wherenotions of structure and independence take on different rolesin reasoning.Our work is most significantly distinguishedfrom work on CSPs(e.g.,[12])and more recently,logical rea-soning(e.g.,[11;25])in that we reason with explicitly par-titioned theories using message passing algorithms and ouralgorithms apply to FOL as well as propositional theories.In the area of FOL theorem proving,our work is relatedto research on parallel theorem proving(see surveys in[6;15])and on combining logical systems(e.g.,[24;4]).Mostparallel theorem prover implementations are guided by looka-head and subgoals to decompose the search space dynami-cally or allow messages to be sent between different proversworking in parallel,using heuristics to decide on which mes-sages are relevant to each prover.These approaches typicallylook at decompositions into very few sub-problems.In addi-tion,thefirst approach typically requires complete indepen-dence of the sub-spaces or the search is repeated on much ofthe space by several reasoners.In the second approach thereis no clear methodology for deciding what messages shouldbe sent and from which partition to which.The work on combining logical systems focuses on combi-nations of signature-disjoint theories(allowing the queries toinclude symbols from all signatures)and decision proceduressuitable for those theories.All approaches either nondeter-ministically instantiate the(newly created)variables connect-ing the theories or restrict the theories to be convex(disjunc-tions are intuitionistic)and have informationflowing backand forth between the theories.In contrast,we focus onthe structure of interactions between theories with signaturesthat share symbols and the efficiency of reasoning with con-sequencefinders and theorem provers.We do not have anyrestrictions on the language besidesfiniteness.Work on formalizing and reasoning with context(see[1] for a survey)can be related to theorem proving with struc-tured theories by viewing the contextual theories as interact-ing sets of theories.Unfortunately,to introduce explicit con-texts,a language that is more expressive than FOL is needed. Consequently,a number of researchers have focused on con-text for propositional logic,while much of the reasoning work has focused on proof checking(e.g.,GETFOL[16]).7SummaryIn this paper we exploited graph-based techniques to im-prove the efficiency of theorem proving for structured the-ories.Theories were organized into subtheories that were minimally connected by the literals they share.We presented message-passing algorithms that reason over these theories using consequencefinding,specializing our algorithms for the case offirst-order resolution,and for batch and concurrent theorem proving.We provided an algorithm that restricts the interaction between subtheories by exploiting the polarity of literals.We attempted to minimize the reasoning within each individual partition by exploiting existing algorithms for fo-cused incremental and general consequencefinding.Finally, we proposed an algorithm that compiles each subtheory into one in a reduced sublanguage.We have proven the soundness and completeness of all of these algorithms.The results pre-sented in this paper contribute towards addressing the prob-lem of reasoning efficiently with large or multiple structured commonsense theories.AcknowledgementsWe wish to thank the anonymous IJCAI reviewers for their thorough review of this paper,and Alvaro del Val and Pierre Marquis for helpful comments on the relationship between our work and previous work on consequencefinding.This research was supported in part by DARPA grant N66001-97-C-8554-P00004,NA VY grant N66001-00-C-8027,and by DARPA grant N66001-00-C-8018(RKF program). 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构成整体所必需的英语English Answer：Definition of Essential:The term "essential" is derived from the Latin word "essentia," which means "being" or "substance." In philosophy, the essential nature of an entity is understood to be the set of fundamental properties that are both necessary and sufficient to constitute the entity as a member of its kind. These properties are typically distinguished from accidental properties, which are not necessary for the entity to exist or to belong to a particular category.Essential Constituents of a Whole:When applied to complex entities, such as wholes, the notion of essentiality becomes more multifaceted. A whole is often composed of multiple parts or components thatcontribute to its overall structure and function. The essential constituents of a whole are those components that are indispensable to its existence and identity. These are the parts without which the whole would either cease to exist or be fundamentally altered.Criteria for Identifying Essential Constituents:Determining which components are essential to a whole can be a complex task. However, there are several general criteria that can be used to guide the analysis:Necessity: An essential constituent is one that is necessary for the whole to exist or to perform its core function. Without this component, the whole would either not come into being or would be unable to fulfill its intended purpose.Sufficiency: In addition to being necessary, an essential constituent must also be sufficient to identify the whole. This means that the presence of the component alone is enough to establish the existence and identity ofthe whole.Irreplaceability: Essential constituents are typically irreplaceable in the sense that they cannot be substituted by other components without altering the nature of the whole. This is because these components play unique and indispensable roles within the overall structure andfunction of the whole.Examples of Essential Constituents:The concept of essential constituents can beillustrated through various examples:The essential constituents of a chair include the seat, backrest, and legs. Without any of these components, the chair cannot fulfill its primary function of providing a place to sit.The essential constituents of an automobile includethe engine, transmission, and wheels. These components are necessary for the automobile to function as a means oftransportation.The essential constituents of a family include the parents and children. These individuals are necessary to form a familial unit and to fulfill the social and emotional functions of a family.Conclusion:The identification of essential constituents is a crucial step in understanding the composition and nature of wholes. By identifying the components that are necessary and sufficient for the existence and identity of an entity, we can gain a deeper understanding of its structure and function.Chinese Answer：本质的定义：术语“本质”源自拉丁语单词“essentia”，意为“存在”或“实体”。