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Forward and Backward Chaining in Linear Logic
"... . Logic programming languages based on linear logic are of both theoretical and practical interest, particulaly because such languages can be seen as providing a logical basis for programs which execute within a dynamic environment. Most linear logic programming languages are implemented using stand ..."
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. Logic programming languages based on linear logic are of both theoretical and practical interest, particulaly because such languages can be seen as providing a logical basis for programs which execute within a dynamic environment. Most linear logic programming languages are implemented using standard resolution or backward chaining techniques. However, there are many applications in which the combination of such techniques with forward chaining ones are desirable. We develop a prooftheoretic foundation for a system which combines both forms of reasoning in linear logic. 1 Introduction Backward chaining is a standard technique in automated deduction, particularly in logic programming systems, often taking the form of a version of Robinson's resolution rule [18]. The fundamental question is to determine whether or not a given formula follows from a given set of formul, and there are various techniques which can be used to guide the search for a proof. An instance of this approach is...
Towards the Automation of the Design of Logic Programming Languages
 Department of Computer Science, RMIT
, 1997
"... Logic programs consist of formulas of mathematical logic and various prooftheoretic techniques can be used to design and analyse execution models for such programs. We briefly review the main problems, which are questions that are still elusive in the design of logic programming languages, from a p ..."
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Cited by 4 (4 self)
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Logic programs consist of formulas of mathematical logic and various prooftheoretic techniques can be used to design and analyse execution models for such programs. We briefly review the main problems, which are questions that are still elusive in the design of logic programming languages, from a prooftheoretic point of view. Existing approaches and analyses which lead to the various languages are all rather sophisticated and involve complex manipulations of proofs. All are designed for analysis on paper by a human and many of them are ripe for automation. We aim to perform the automation of some aspects of prooftheoretic analyses, in order to assist in the design of logic programming languages. In this paper we describe the first steps towards the design of such an automatic analysis tool. We investigate the usage of particular proof manipulations for the analysis of logic programming strategies. We propose a more precise specification of sequent calculi inference rules that we use ...
MetaTheory of SequentStyle Calculi in Coq
, 1997
"... We describe a formalisation of proof theory about sequentstyle calculi, based on informal work in [DP96]. The formalisation uses de Bruijn nameless dummy variables (also called de Bruijn indices) [dB72], and is performed within the proof assistant Coq [BB + 96]. We also present a description of ..."
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We describe a formalisation of proof theory about sequentstyle calculi, based on informal work in [DP96]. The formalisation uses de Bruijn nameless dummy variables (also called de Bruijn indices) [dB72], and is performed within the proof assistant Coq [BB + 96]. We also present a description of some of the other possible approaches to formal metatheory, particularly an abstract named syntax and higher order abstract syntax. 1 Introduction Formal proof has developed into a significant area of mathematics and logic. Until recently, however, such proofs have concentrated on proofs within logical systems, and metatheoretic work has continued to be done informally. Recent developments in proof assistants and automated theorem provers have opened up the possibilities for machinesupported metatheory. This paper presents a formalisation of a large theory comprising of over 200 definitions and more than 500 individual theorems about three different deductive system. 1 The central dif...
Strategies for Logic Programming Languages
"... . Logic programs consist of formulas of mathematical logic and various prooftheoretic techniques can be used to design and analyse execution models for such programs. We briefly review the main problems, which are questions that are still elusive in the design of logic programming languages, from a ..."
Abstract
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. Logic programs consist of formulas of mathematical logic and various prooftheoretic techniques can be used to design and analyse execution models for such programs. We briefly review the main problems, which are questions that are still elusive in the design of logic programming languages, from a prooftheoretic point of view. Existing strategies which lead to the various languages are all rather sophisticated and involve complex manipulations of proofs. All are designed for analysis on paper by a human and many of them are ripe for automation. We aim to perform the automation of some aspects of strategies for logic programming language, in order to assist in the design of these languages. In this paper we describe the first steps towards the design of such an automatic analysis tool. We investigate the usage of particular proof manipulations for the analysis of logic programming strategies. We propose a more precise specification of sequent calculi inference rules that we use as a ...