Results 1 
4 of
4
GoalDirected Proof Search in MultipleConclusioned Intuitionistic Logic
 In Proceedings of the First International Conference on Computational Logic, volume LNAI 1861
, 2000
"... . 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 (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multip ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
. 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 (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multipleconclusioned systems such as those for linear logic. Given these developments, it seems interesting to investigate the notion of goaldirected proofs for a multipleconclusioned sequent calculus for intuitionistic logic, in that this is a logic for which there are both singleconclusioned and multipleconclusioned systems (although the latter are less well known). In this paper we show that the language obtained for the multipleconclusioned system differs from that for the singleconclusioned case, show how hereditary Harrop formulae can be recovered, and investigate contractionfree fragments of the logic. 1 Introduction Logic programming is based upon the observation that if ...
On GoalDirected Proofs in MultipleConclusioned 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 (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multiple ..."
Abstract
 Add to MetaCart
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 (singleconclusioned) sequent calculus LJ, but has subsequently been adapted to multipleconclusioned systems such as those for linear logic. Given these developments, it seems interesting to investigate the notion of goaldirected proofs for a multipleconclusioned sequent calculus for intuitionistic logic, in that this is a logic for which there are both singleconclusioned and multipleconclusioned systems (although the latter are less well known than the former). In this paper we show that the language obtained for the multipleconclusioned system differs from that for the singleconclusioned case, and discuss the consequences of this result. Keywords: Multipleconclusioned intuitionistic logic, goaldirected proofs, logic programming languages, hereditary Harrop formu...
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
 Add to MetaCart
. 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 ...
Search Calculi for Classical and Intuitionistic Logic
"... Abstract. It is wellknown that inference rules in the sequent calculus can be interpreted as both proof construction rules (i.e. constructing proofs from the leaves towards the root of the tree) and proof search rules (i.e. finding proofs by starting at the (supposed) root and working towards the l ..."
Abstract
 Add to MetaCart
Abstract. It is wellknown that inference rules in the sequent calculus can be interpreted as both proof construction rules (i.e. constructing proofs from the leaves towards the root of the tree) and proof search rules (i.e. finding proofs by starting at the (supposed) root and working towards the leaves). However, the information used in each case is different: the former constructs larger proofs from smaller ones, whereas the latter constructs search trees, from which, if the search is successful, a proof can be recovered. Thus during search the intermediate stages are at best partial proofs. In this paper we explore a variation of the sequent calculus in which search information, in the form of Boolean constraints, is added to each sequent. In particular, we show how this can be done for the sequent calculus LK for classical logic and the multipleconclusioned sequent LM for intuitionistic logic. In addition, we show how a judicious use of hypersequents can improve the search properties of LM. 1