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Fixpoint semantics for logic programming a survey

Melvin Fitting
2002 Theoretical Computer Science  
The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology.  ...  Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities  ...  Acknowledgement I want to thank Howard Blair for a number of suggestions that improved the presentation in this paper.  ... 
doi:10.1016/s0304-3975(00)00330-3 fatcat:ec6vntnnu5eoflpgohb3qz5ylm

Intensional logics

Irene Guessarian
1995 Science of Computer Programming  
Parts III and IV of the book are concerned with propositional dynamic logic, theory of deterministic morphisms, duality of forward and reverse predicate transformers, threevalued logics, and distributive  ...  To conclude, this book is a very nice survey and shows quite a few case studies of how non-classical logics can help in the study of logic programs and their semantics.  ...  Subrahmanian presents in an illuminating way a general framework of monotone abstract logics for studying the semantics of programs.  ... 
doi:10.1016/0167-6423(95)90015-2 fatcat:brid6oph4bgtxh43wvakmby7km

Page 3762 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
The aim of the paper is to examine infinite derivations in ‘pure’ logic programming, and to provide a greatest fixpoint semantics of logic programs as a set of co-inductive definitions.  ...  Herbrand constraints provide an adequate model for logic programming semantics.  ... 

Page 3368 of Mathematical Reviews Vol. , Issue 92f [page]

1992 Mathematical Reviews  
The declarative semantics of stratifiable logic programs is defined by means of iter- ative fixpoints. Section 5 is devoted to the well-founded semantics of logic programs.  ...  Section 3 includes a brief introduction of the model-theoretic and the fixpoint semantics of positive logic programs (sets of definite clauses).  ... 

Abstract interpretation

Patrick Cousot
1996 ACM Computing Surveys  
as a parameter, either that of the program to be analyzed or that of a programming language.  ...  We review how the dependence upon semantics has been taken into account in abstract interpretation based program analysis and next propose to design general purpose abstract interpreters taking semantics  ...  This is quite effective for imperative, logic, constraint, functional (e.g. through term graph rewriting or interaction nets) and shared or distributed parallel programming languages, but fails for the  ... 
doi:10.1145/234528.234740 fatcat:7sf2zvjdfrcnxmggblh7bgs6mm

The optimal model of a program with negation [chapter]

J. P. Delahaye, V. Thibau
1991 Lecture Notes in Computer Science  
As the models of a program are exactly the post-fixpoints of this operator, the first provided denotational semantics of a program is the least fixpoint semantics.  ...  Abstact: The aim of this paper is to provide another denotational semantics than the least firpoint semantics for a logic program with negation.  ...  For a good survey on negation in logic programming, the reader is sent to [4d] .  ... 
doi:10.1007/bfb0018441 fatcat:ppirqfygqfeq7anweuli24j67i

Datalog Unchained

Victor Vianu
2021 Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems  
These languages also provide a unified formalism that can express important classes of queries including fixpoint, while, and all computable queries.  ...  This is the companion paper of a talk in the Gems of PODS series, that reviews the development, starting at PODS 1988, of a family of Datalog-like languages with procedural, forward chaining semantics,  ...  Special thanks to Serge Abiteboul for revisiting our joint work and providing many useful suggestions for the presentation.  ... 
doi:10.1145/3452021.3458815 fatcat:b6mnoptf2jgdtl27xrt54z7r5u

Approximation Fixpoint Theory and the Semantics of Logic and Answers Set Programs [chapter]

Marc Denecker, Maurice Bruynooghe, Joost Vennekens
2012 Lecture Notes in Computer Science  
for defining natural and elegant versions of these semantics for extensions of logic and answer set programs.  ...  Approximation Fixpoint Theory was developed as a fixpoint theory of lattice operators that provides a uniform formalization of four main semantics of three major nonmonotonic reasoning formalisms.  ...  The names of these fixpoints reflect the well-known semantics of logic programming.  ... 
doi:10.1007/978-3-642-30743-0_13 fatcat:gxsf3zh7yzedhnoaaj6qhwszr4

Temporal Logics Beyond Regularity

Martin Lange
2007 BRICS Report Series  
In particular, it features Propositional Dynamic Logic of Context-Free Programs, Fixpoint Logic with Chop, the Modal Iteration Calculus, and Higher-Order Fixpoint Logic.  ...  This thesis surveys results about the relative expressive power and complexity of temporal logics which are capable of defining non-regular properties.  ...  PDL The Modal Iteration Calculus Fixpoint Logic with Chop Higher-Order Fixpoint Logic The Semantics of FLC lift semantics of modal µ-calculus to space of monotone functions of type 2 S → 2 S ,  ... 
doi:10.7146/brics.v14i13.22178 fatcat:s4wi6d5ewffnrpew3leughbmhm

A fixpoint characterization of abductive logic programs

Katsumi Inoue, Chiaki Sakama
1996 The Journal of Logic Programming  
A new fixpoint semantics for abductive logic programs is provided, in which the belief models of an abductive program are characterized as the fixpoint of a disjunctive program obtained by a suitable program  ...  The result is further generalized to a fixpoint semantics for abductive extended disjunctive programs.  ...  An inter- FIXPOINT THEORY FOR ABDUCTIVE LOGIC PROGRAMS This section presents a fixpoint semantics for abductive normal logic programs.  ... 
doi:10.1016/0743-1066(95)00119-0 fatcat:hoq2n3pjnneslc3bbl7iwta7ju

Page 2865 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
{For the entire collection see MR 2002m:03003.} 2003d:68019 68N17 03B70 68N15 68Q55 Fitting, Melvin (1-CUNY7; Bronx, NY) Fixpoint semantics for logic programming a survey.  ...  Summary: “An elementary formal system (EFS) is a logic program such as a Prolog program, for instance, that directly manipulates strings.  ... 

On Greatest Fixpoint Semantics of Logic Programming

M. Jaume
2002 Journal of Logic and Computation  
Hence, since defining a greatest fixpoint semantics for logic programs amounts to consider a program as a set of co-inductive definitions, we focus on this identification at a deeper level by considering  ...  The study of fixpoints has long been at the heart of logic programming.  ...  Acknowledgements Many thanks to René Lalement, Catherine Dubois and Baudouin Le Charlier for enlightening discussions about this work, as well as the anonymous referees for some very useful comments.  ... 
doi:10.1093/logcom/12.2.321 fatcat:r6qj3gly45gpvc3wtntykmwgre

Datalog with non-deterministic choice computes NDB-PTIME

Fosca Giannotti, Dino Pedreschi
1998 The Journal of Logic Programming  
We refer to [4] for a comprehensive discussion on programming with nondeterminism in deductive databases.  ...  A first batch of proposals is due to Abiteboul and Vianu [6, [9] [10] [11] , based on a non-deterministic witness construct for the fixpoint extensions of FO, and a non-deterministic operational semantics  ...  Thanks are also owing to Victor Vianu, Luigi Palopoli, Carlo Zaniolo and Mimmo Sacc~ for their useful suggestions on the subject of this paper.  ... 
doi:10.1016/s0743-1066(97)10004-8 fatcat:nu7u6i6qjjhkble22k2sbobqim

Author index volume 278 (2002)

2002 Theoretical Computer Science  
., Fixpoint semantics for logic programming a survey (1-2) 25-51 Flagg, R.C. and P.  ...  Saraswat, Truly concurrent constraint programming (1-2) 223-255 Hennessy, M., A fully abstract denotational semantics for the p-calculus (1-2) 53-89 Jagadeesan, R., see V.  ... 
doi:10.1016/s0304-3975(02)00149-4 fatcat:aatd2uip3nfazmcqnx5bzq6obq

Possible Worlds Semantics for Probabilistic Logic Programs [chapter]

Alex Dekhtyar, Michael I. Dekhtyar
2004 Lecture Notes in Computer Science  
In particular, we propose a new semantics, for the Probabilistic Logic Programs (p-programs) of Ng and Subrahmanian. P-programs represent imprecision using probability intervals.  ...  In this paper we consider a logic programming framework for reasoning about imprecise probabilities.  ...  First, we describe the possible worlds semantics for a simple logic programming language in which probability intervals are associated with each atom in a program (simple pprograms) (Section 2).  ... 
doi:10.1007/978-3-540-27775-0_10 fatcat:yh7pvd335jfyhaeytotneppyhy
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