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**11 - 13**of**13**### On Goal-Directed Proofs in Multiple-Conclusioned Intuitionistic Logic

"... A key property in the definition of logic programming languages is the completeness of goaldirected proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (single-conclusioned) sequent calculus LJ, but has subsequently been adapted to multiple- ..."

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A key property in the definition of logic programming languages is the completeness of goaldirected proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (single-conclusioned) sequent calculus LJ, but has subsequently been adapted to multiple-conclusioned systems such as those for linear logic. Given these developments, it seems interesting to investigate the notion of goal-directed proofs for a multipleconclusioned sequent calculus for intuitionistic logic, in that this is a logic for which there are both single-conclusioned and multiple-conclusioned systems (although the latter are less well known than the former). In this paper we show that the language obtained for the multiple-conclusioned system differs from that for the single-conclusioned case, and discuss the consequences of this result. Keywords: Multiple-conclusioned intuitionistic logic, goal-directed proofs, logic programming languages, hereditary Harrop formu...

### Strategies for Logic Programming Languages

"... . Logic programs consist of formulas of mathematical logic and various proof-theoretic 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 ..."

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. Logic programs consist of formulas of mathematical logic and various proof-theoretic 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 proof-theoretic 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 ...

### Logic Programming in Affine Logic

, 1995

"... Traditional logic programming languages, such as Prolog, apply the methods of classical logic to programming tasks. Recently, computer scientists introduced new logic programming languages, based on linear logic rather than classical logic. While classical logic models information that does not chan ..."

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Traditional logic programming languages, such as Prolog, apply the methods of classical logic to programming tasks. Recently, computer scientists introduced new logic programming languages, based on linear logic rather than classical logic. While classical logic models information that does not change, linear logic models changes of state, and accounts for finite resources, such as money or computer memory, simply and directly. It has been applied to concurrency, natural language processing, updating information in databases, and other resource-sensitive problems. Affine logic is related to linear logic and has a similar range of applications but with a different emphasis. In a linear logic system, axioms mean that a particular resource is spent to meet a particular requirement, and every formula must be used, or spent, exactly once. This makes linear logic ideal for accounting for all resources. However, some situations require resources to be used at most once. Affine logic captures this notion because using all resources is not necessary. Therefore, programming languages based on affine logic may prove to be useful. To investigate how affine logic may be applied to logic programming, it is necessary to specify the differences between affine logic and classical logic, and between affine logic and linear logic. This paper looks at these differences in terms of the "structural" rules of classical logic. Keywords: affine logic, linear logic, logic programming 1.