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A Proof Theoretic Approach to Failure in Functional Logic Programming [article]

Francisco Javier Lopez-Fraguas, Jaime Sanchez-Hernandez
2004 arXiv   pre-print
How to extract negative information from programs is an important issue in logic programming. Here we address the problem for functional logic programs, from a proof-theoretic perspective.  ...  We present a proof calculus, CRWLF, which is able to deduce negative information from CRWL-programs. In particular, CRWLF is able to prove finite failure of reduction within CRWL.  ...  Some natural future steps are to develop model theoretic and operational semantics for programs making use of failure information.  ... 
arXiv:cs/0405102v1 fatcat:gvyqaynnvfeajnv3aeaneuile4

Page 8159 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
(E-MADC-PG; Madrid) ; Sanchez-Hernandez, Jaime (E-MADC-PG; Madrid) A proof theoretic approach to failure in functional logic programming. (English summary) Theory Pract. Log.  ...  The present paper addresses the problem of extracting negative information in the framework of functional logic programming (FLP) from a proof-theoretic perspective.  ... 

Page 7455 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
Closure condi- tions and inductive definitions are extended to three-valued struc- tures. The first proof-theoretic approach is introduced by a sequent calculus LK, for first-order logic.  ...  To that end a modest extension to the functional calculus is proposed, including partial functions, and a few simple high level programming constructs are introduced.  ... 

Page 2867 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
This approach involves a similarity relation & between function and predicate symbols in the language of a logic program.  ...  This parameterization can be obtained at a basic level using higher order functions as described in Cousineau and M. Mauny [The functional approach to programming, Cambridge Univ.  ... 

Proving Failure in Functional Logic Programs [chapter]

Francisco J. López-Fraguas, Jaime Sánchez-Hernández
2000 Lecture Notes in Computer Science  
How to extract negative information from programs is an important issue in logic programming. Here we address the problem for functional logic programs, from a proof-theoretic perspective.  ...  We present a proof calculus, CRWLF, which is able to deduce negative information from CRWL-programs. In particular, CRWLF is able to prove 'finite' failure of reduction within CRWL.  ...  Failure in logic programs, when seen as functional logic programs, corresponds to failure of reduction to 'true'.  ... 
doi:10.1007/3-540-44957-4_12 fatcat:c73vihx2xjdivonazpkuruvyou

Page 3764 of Mathematical Reviews Vol. , Issue 86h [page]

1986 Mathematical Reviews  
[Maher, Michael John] (5-MELB) Closures and fairness in the semantics of programming logic. Theoret. Comput. Sct. 29 (1984), no. 1-2, 167-184.  ...  Author summary: “We use the notions of closures and fair chaotic iterations to give a semantics to logic programs.  ... 

Regular search spaces as a foundation of logic programming [chapter]

Alberto Momigliano, Mario Ornaghi
1994 Lecture Notes in Computer Science  
First, we aim to provide a proof-theoretic reconstruction of logic programming, both for definite and for normal programs.  ...  This leads us to a better understanding of negation-as-failure (NF) [5] and of other proof-theoretically well-founded extensions of Prolog.  ...  We would like to thank Roy Dyckhoff and Frank Pfenning for their valuable comments on earlier versions of this paper.  ... 
doi:10.1007/3-540-58025-5_59 fatcat:7okk6khlq5gozo7wydffw5hqxe

A Model-Theoretic Semantics for Defeasible Logic [article]

Michael J. Maher
2002 arXiv   pre-print
In this paper a model-theoretic semantics is given for defeasible logic. The logic is sound and complete with respect to the semantics.  ...  We also briefly outline how this approach extends to a wide range of defeasible logics.  ...  Billington, who introduced me to the problem of defining a model theory for defeasible logic, and gave me access to his extensive library of papers on defeasible logic, and to G. Antoniou and G.  ... 
arXiv:cs/0207086v1 fatcat:etr7skifcvd3rjpb4csdfzwxdy

Editorial

Hélène Kirchner, Wolfgang Wechler
1992 Theoretical Computer Science  
This paper is concerned with the pure logical approach, and its specific interest lies in the relationship between the two most successful approaches to the semantics of negation in logic programming.  ...  This approach addresses a quite interesting integration of concurrent logic programming with constraint logic programming.  ... 
doi:10.1016/0304-3975(92)90283-l fatcat:nb6jl2blyrfg3pkdq6yrch5wwi

Page 4890 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
This leads us to a better understanding of negation- as-failure and of other proof-theoretically well-founded extensions of Prolog.  ...  Summary: “First, we aim to provide a proof-theoretic recon- struction of logic programming, both for definite and for normal programs.  ... 

Some issues and trends in the semantics of logic programming [chapter]

J. Jaffar, J -L. Lassez, M. J. Maher
1986 Lecture Notes in Computer Science  
In a second part we consider extensions to definite clause logic programs.  ...  This results in a formalism which brings the theory of logic programming closer to standard programming practice.  ...  Furthermore, the algebraic and logical approaches also coincide for canonical programs. A formal presentation of these results is to be found in Jaffar and Lassez [12] .  ... 
doi:10.1007/3-540-16492-8_78 fatcat:ly6owdbvyrdszkrao3u5hx2w4u

Proof-theoretic notions for software maintenance

Reinhard Kahle
2001 Electronical Notes in Theoretical Computer Science  
We discuss proof-theoretic notions as a useful tool to deal with software maintenance in a formal setting.  ...  In such a system the consequences of a change of a program is much harder to control. In logic programming we face this problem if we work with closed world assumption or negation as failure.  ...  Studer has even used this framework to deal with the functional core of the programming language Java [35] . In logic programming which is based on resolution, cf.  ... 
doi:10.1016/s1571-0661(05)80048-9 fatcat:xue7emzwobejvavmyxvkzwsnoa

Linear logic semantics for Concurrent Prolog [chapter]

Jiří Zlatuška
1994 Lecture Notes in Computer Science  
This paper develops a proof-theoretic semantics based on linear logic for Concurrent Prolog.  ...  Several fragments of linear logic are used in order to provide for a suitable translation of Concurrent Prolog clauses, with the committed-choice concurrency features captured by the properties of linear  ...  Proof-theoretic semantics views logic program execution as a process of proof synthesis.  ... 
doi:10.1007/3-540-58025-5_66 fatcat:fgrkokatfnduneiit5utujalia

Page 4343 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
“Formulas as programs is argued to yield a realistic approach to programming that has been realized in the implemented program- ming language Alma-0 that combines the advantages of imperative and logic  ...  In this approach the formulas themselves are programs. This contrasts with the so-called formulas as types approach in which the proofs of the formulas are typed terms that can be taken as programs.  ... 

Page 2046 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
In order to achieve a sys- tematic treatment, we need to review a number of elementary definitions from logic and theoretical computer science and adapt them to the needs of logic programming.  ...  Logical semantics also provides a natural approach, through proof systems, to verifiably correct implementations that is sometimes simpler than the denotational and algebraic approaches.  ... 
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