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LOGIC PROGRAM DERIVATION FOR A CLASS OF FIRST ORDER LOGIC RELATIONS

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LOGIC PROGRAM DERIVATION FOR A CLASS OF FIRST ORDER LOGIC RELATIONS

George Dayantis *

Cognitive Studies Division, University of Sussex

Falmer, Brighton, BN1 9QN

G. BRITAIN

ABSTRACT

Logic programming has been an attempt to bridge

the gap betwen specification and programming language

and thus to simplify the software development process.

Even though the only difference between a specification

and a program in a logic programming framework is that

of efficiency, there is still some conceptual distance to

be covered between a naive, intuitively correct

specification and an efficiently executable version of it

And even though some mechanical tools have been

developed to assist in covering this distance, no fully

automatic system for this purpose is yet known. In this

paper v/t present a general class of first-order logic rela-

tions, which is a subset of the extended Horn clause

subset of logic, for which we give mechanical means for

deriving Horn logic programs, which are guaranteed to

be correct and complete with respect to the initial

specifications.

I. INTRODUCTION

A* Logic program derivation*

Logic programming is an attempt to bridge the gap

between specification and programming language

requirements. By making a clear separation between

logic and control, it makes it possible for the program-

mer to deal initially with the logic of his problem and

then derive more efficient, still logically equivalent, ver-

sions of it by altering the control accordingly. The

apparently simple operational semantics of Horn-clausal

logic and its various efficient implementations, mainly in

the form of PROLOG interpreters and compilers, makes

it quite appealing as a programming language.

Of course, even though it has been shown that any

problem expressed in first oider predicate logic can be

reformulated using only Horn clauses, expressing prob-

lems in Horn clauses is certainly not claimed to be very

natural. Various attempts have been made - [Bowen

1982], [Murray 1982], [Stickel 1984] - to implement full

first-order logic as a programming language but, apart

from efficiency considerations, the lack of intuitively

clear operational semantics for full first-onier logic

makes them unusable.

On the other hand, [Clark & Sickel 1977], [Hannson

* Research supported by the Greek Slate Scholarships Foundation.

Dayantis 9

Some of the inference steps presented here and

other more complex ones needed for more difficult

derivations can be easily mechanised, but there remains

a significant portion of them, -which seems to require

some inventiveness. It should be emphasised here that

no complete inference system exists yet for such deriva-

tions. The same applies to transformation techniques

for improving the efficiency of logic programs.

Thus, although deduction is a logically sufficient

tool for creating logic programs from specifications or

from other programs, this tool requires intelligent con-

trol in order to be practicaL An attempt towards the

implementation of a semi-automatic tool for assisting

with such manipulations is reported in [Vasey 1985]. In

this paper, however, -we restrict our attention to a

specific class of relations, -which -we identify in section II

and, for -which fully automatic program derivation is

possible, as we shall show. And because -we find that a

systematic treatment of data types in bgic is necessary

for the adequate formalisation of our results, -we present

such a treatment below.

B. Characterising data types in logic

Clark and Tamlund in [Clark & Tamlund 1977]

were the first ones to present a uniform way to charac-

terise and deal with data types within the framework of

first-order logic. Different treatments of data types in

bgic also appear in [Vasey 1985]. Here, however, we

restrict our attention to recursively defined data types

and present a general axiomatic way of characterising

them, which serves as the basis for formalising some

results in the next section.

By data type - or sort - we mean a collection of

values, a subset of the Herbrand Universe. A simple

way to characterise data types without departing from

first-order bgic is to use predicates, since any relation

can be thought of as defining data types for its argu-

ments ,Le. the sets of values that bebng to the relation.

For example, consider the unary predicate natural, such that is true if and only if is a natural

number - bebngs to the data type natural This data type can be axiomatised with a recursive definition: exor (naturul(y) & JO- sucdy)) and an equality axiom:

where exor is the symbol for exclusive or, 1 is a con-stant and is the successor function; 1 and are

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Lexicology

Lexicology

Lexicology(英语词汇学 英语词汇学) English Lexicology(英语词汇学) : Lexicology 词汇学） is

a

branch of linguistics, inquiring into the origins （词汇学） and meanings of words. lexicology：

The

Nature and Scope of English lexicology English lexicology aims at investigating and studying the

morphological structures of English words and word equivalents, their semantic structures, relations,

historical development, formation and usages. to：

The subjects that English Lexicology correlated

with and extent to English Lexicology is correlated with such linguistic disciplines as morphology(形态学), semantics(语义学), etymology(词源学),stylistics（文 体论） and lexicography(词典学)

lexicology：

The reason for a student to study English lexicology According to the textbook, English

Lexicology will definitely be beneficial for students of English. A good knowledge of morphological

arbitrary语言学例子

arbitrary语言学例子

arbitrary语言学例子

语言学概论

1. Language—a system of arbitrary vocal symbols used for

human communication

2. Nature of language

Arbitrary. Systematic. Vocal. Symbolic. human specific for

communication

3. Design features of language

① Productivity/creativity. produce or understand

indefinite sentences by using finite set of rules

② Duality. Sounds and meaning system

③ Arbitrariness: no connection between words and

meanings.

④ Displacement. overcome barriers caused by space and

time

⑤ Transferability. Spoken and read, transfer into each

other.

⑥ Cultural transmission：Language and culture are closely

connected. Languages are parts of culture， reflect culture and

pass on from generation to generation by learning

4. Function of language ① informative function(最重要)

② phatic function—maintain social relationship

③ recording function

语言学术语英文表达

语言学术语英文表达

语言学作业

CHAPTER 1

Design features refers to the defining properties of human language, including arbitrariness,

duality, creativity and displacement.

Function may be practical. For example, we use language to chat, to think, to buy and sell, to read

and write, to greet, praise and condemn people, etc. But linguists talk about FUNCTIONS of

language in an abstract sense and attempt some broad classifications of the basic functions of

language like the following: informative, interpersonal function, performative function, emotive

function, phatic function, recreational function, metalingual function.

Synchronic: Synchronic linguistics is the study of a language at one particular point in time

Diachronic: Diachronic linguistics studies how a language changes over a period of time

Descriptive: to describe the fact of linguistic usage as they are, and not how they ought to be, with

语言学教程胡壮麟（第四版）第3章

语言学教程胡壮麟（第四版）第3章

语⾔学教程胡壮麟（第四版）第3章

Chapter 3 From Morpheme to Phrase

第⼀部分The formation of word——Morpheme词的构成1. Morpheme 词素的定义

Morpheme is the smallest meaningful unit of language in regard to the relationship between sounding and meaning, a unitthat cannot be divided into further smaller units without destroying or drastically altering the meaning, such as boy and –s inboys, check and –ing in checking. And the systematic study of morpheme is a branch of linguistics called morphology

2. Types of morphemes 词素的种类

①Free morpheme and bound morpheme ⾃由词素和黏着词素

Free morphemes: Those that may occur alone, that is, those which may make up words by themselves, are free morphemes,such as Dog, nation.

Bound morphemes: Those that cannot occur alone. They must appear with at least one different morpheme, are called boundmorphemes, for example, the word distempered has three morphemes, namely, dis-, temper, and –ed, of which temper is afree morpheme, dis- and –ed are two bound morphemes.