Fixpoint semantics for logic programming pdf

A fixpoint semantics and an sldresolution calculus for. Fixpoint characterizations for manyvalued disjunctive logic. Fixpoint characterizations for manyvalued disjunctive. Pdf the stable model semantics for logic programming. In general, the semantics are the coded algorithms. Bibtex does not have the right entry for preprints. The authors did proofread thoroughly, while the editors and referees did not criticize adequatelythe recent memorandum from the computer science board requesting attentiveness to duties is illustrated here.

The paper is a general overview of our approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semantics based program analysis. This can then be used to show that, in logic programming, certain transformations are equivalence preserving under, among others, both the stable and wellfounded semantics. The key difference with the semantics proposed by moore is that we consider approximations of possibleworld structures by pairs of. Since logic programming computation is proof search, to study logic programming means to study proofs. Fixpoint semantics for logic programming a survey request pdf. First, it proposes a sound and complete proof system for matching logic in its full generality. This is a hack for producing the correct reference. Execution of a logic program is a theorem proving process. It is concluded that operational semantics is a part of proof theory and that fixpoint semantics is a special case of modeltheoretic. We show with examples of logic programs which have a unique stable model but. Theoretical foundations and semantics of logic programming. Fixpoint 3valued semantics for autoepistemic logic marc denecker1, v. Logic programming, fundamenta informaticae on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.

An excellent survey of fixpoint semantics for logic programming is fit99. Fitting 5 uses this approach to present an alternative to the semantics of logic programming given by apt and van emden 2. The key difference with the semantics proposed by moore is that we consider approximations of possibleworld structures by pairs of possibleworld for. However, he did not provide a fixpoint theory for such class of databases. Unfolding and fixpoint semantics of concurrent constraint. Fixpoint semantics for a fragment of firstorder linear logic marco bozzano may 22, 2001 cmucs01129 school of computer science carnegie mellon university pittsburgh, pa 152 disi, universit a di genova, italy abstract in this paper we investigate the theoretical foundation of a bottomup, xpoint semantics for a subset of girards linear. Covering the authors own stateoftheart research results, mathematical aspects of logic programming semantics presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. As an application of our framework, we also present a formal investigation of the relations between lo and disjunctive logic programming. The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology.

The study of fixpoints has long been at the heart of logic programming. Fixpoint semantics and optimization of recursive datalog programs. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. Nonetheless, much of the work on logic programming semantics.

Mathematical aspects of logic programming semantics. We extend the concept of the herbrand base of a logic program to consist of all positive clauses that may be formed using the atoms in the herbrand base. Scotland abstract sentences in firstorder predicate logic can be usefully interpreted as programs in this paper the. Fixpoint semantics and optimization of recursive datalog. We first give declarative semantics for templog, in modeltheoretic and in fixpoint terms.

Pdf a fixpoint semantics for disjunctive logic programs. Unfolding is also used to define an immediate consequences operator and, therefore, a fixpoint semantics in the typical logic programming style. Pdf fixpoint semantics for logic programming a survey. What the program does during execution time of the code, thats the semantics of the code. A fixpoint 3valued semantics for autoepistemic logic our semantics for autoepistemic logic is defined in terms of possibleworld structures and fixpoint conditions.

On the other hand, nonrecursive rule r 1 with path as its head will be called an exit rule. A pure logicprogrammingbased semantics is not adequate to account for the behavior of sieve. The semantics we present, starting in the next section, is still a. The main contribution of this paper is to show that this approach can also successfully explain the meaning of conditional rewriting systems with negation, including. Pdf predicate introduction for logics with a fixpoint. Then, a denotational semantics of the equivalent, propositional, and infinite dlp program groundp, provides a. Benson this is a sloppily written attempt to provide a general semantics for nondeterministic data flow networks. A fixpoint characterization of abductive logic programs katsumi inoue and chiaki sakama t t 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 transformation.

A new fixpoint semantics for general logic programs. Sentences in firstorder predicate logic can be usefully interpreted as programs. Having attended the first year courses on prolog and constraint logic programming and on programming languages semantics can be useful. This volume contains the papers presented at wlp 2015. A fixpoint semantics and an sldresolution calculus for modal. Pdf we propose a new declarative semantics for logic programs with negation. In this paper we summarize one variety of approaches to the semantics of logic programs. A fixpoint semantics and an sldresolution calculus for modal logic programs a fixpoint semantics and an sldresolution calculus for modal logic programs nguyen, linh anh 20030101 00. A fixpoint semantics for stratified databases springerlink.

Przymusinski extended the notion of stratified logic programs, developed by apt, blair and walker, and by van gelder, to stratified databases that allow both negative premises and disjunctive consequents. In 3, 4, it was shown that all main semantics of logic programming, autoepistemic logic and default logic can be characterized in terms of these. Approximation fixpoint theory and the wellfounded semantics. I have never heard speaking about the semantics of a logic. However, it has also another important application. In section 3, we will recall how autoepistemic logic. A fixpoint semantics for nondeterministic data flow. In this paper the operational and fixpoint semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated. In a companion paper, we developed an algebraic theory that considers predicate introduction within the framework of approximation theory, a fixpoint theory for nonmonotone operators that generalizes all main semantics of various nonmonotonic logics, including logic programming, default logic and autoepistemic logic. An application of the fixpoint operator can be computed algorithmically. Fixpoint semantics for a fragment of firstorder linear logic. Fixpoint semantics for logic programs cs240b notes notes based on section 8. A game semantics for disjunctive logic programming thanos tsouanas1. Although he studied logic as a basis for functional programming rather than logic programming, his ideas are more fundamental and therefore equally applicable in both paradigms.

Then, we study its operational semantics and prove. As mentioned above, the semantics we propose can be applied to approximate the skeptical mode of autoepistemic reasoning. Fixpoint 3valued semantics for autoepistemic logic 3 to determine the truth value of a formula under our semantics is in the class. Semantics for active integrity constraints using approximation fixpoint theory bart bogaertsy and lu s cruzfilipez y ku leuven, department of computer science celestijnenlaan 200a, leuven, belgium z university of southern denmark, department of mathematics and computer science campusvej 55, odense, denmark bart. Predicate introduction for logics with fixpoint semantics. Second, it proposes matching mulogic, an extension of matching logic with a least fixpoint mubinder.

In this paper, we propose a simple comprehensive solution that extends the declarative leastfixpoint semantics of horn clauses, along with the optimization techniques used in the bottomup. Fixpoint semantics and optimization of recursive datalog programs with aggregates. In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages. The reader can find in 5 some examples which further. An excellent survey of xpoint semantics for logic programming is 11. A very desirable datalog extension investigated by many researchers in the last 30 years consists in allowing the use of the basic sql aggregates min, max, count and sum in recursive rules. Fixpoint semantics for logic programming a survey article in theoretical computer science 27812. Fixpoint semantics and optimization of recursive datalog programs with aggregates 3 a goal. So far we have kept syntax and semantics rather informal but, in metalogic we want to prove things about logic this requires us to get really precise about syntax and semantics we are going to give syntax and semantics of propositional logic a mathematical treatment this is called formal syntax and formal semantics. Proceedings of the 29nd workshop on constraint logic. However, whereas least fixpoint semantics works well for sldrefutations i. May 30, 2018 bibtex does not have the right entry for preprints.

Indeed, it will allow both prime2, 3 and prime3, 3 to be part of the meaning of prime. A fixpoint semantics and an sldresolution calculus for modal logic programs linh anh nguyen institute of informatics university of warsaw ul. On the semantics of temporal logic programming preliminary. The predicates in these examples are intended to suggest the use of a many sorted. The semantics we present, starting in the next section, is still a fixpoint semantics. As such, it allows properties of these different semantics for all of these logics to be studied in a uniform way. Approximation theory we use the following notations. Leeuven, celestijnenlaan 200a, b3001 heverlee, belgium 2 department of computer science, university of kentucky, lexington, ky 405060046, usa dedicated to ray reiter on his 60th birthday abstract. On greatest fixpoint semantics of logic programming mi sanu. Read predicate introduction for logics with a fixpoint semantics. Fixpoint and modeltheoretic semantics of logic programs with respect to herbrand interpretations generalize to these semantics for relational programs with respect to finterpretations. The term cannot denote the rules for the logic, because these rules are formal rules without semantics. Programs are written in the language of some logic.

Previously, sound and complete deduction for matching logic was known only for particular theories providing equality and membership. Predicate introduction for logics with a fixpoint semantics. Nonmonotonic logic is now seen as a close relative of logic programming, and developments in either area tend to a. A fixpoint semantics for disjunctive logic programs.

An effective fixpoint semantics for linear logic programs. Fixpoint semantics for logic programming a survey melvin fittinga. Fixpoint semantics for logic programming a survey sciencedirect. Conclusion for arbitrary sentences x and y of firstorder predicate logic, proof theory determines when x y and model theory determines when x y. Prolog programming in logic is a representative logic language. In such a case that the evaluation would be of syntactically invalid strings, the result would be non. Some follow the modeltheoretic approach of formal logic, and some are more like the xpoint. 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. A note on logic programming fixedpoint semantics eprints soton. Since logic programming involves both logic and programming, it should not be surprising that several varieties of semantics have been developed for it. Basics about operational semantics rewriting rules and inference rules and a certain taste for programming are required for this course. We give a fixpoint semantics and an sldresolution calculus for.

As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional lo. A pure logic programming based semantics is not adequate to account for the behavior of sieve. We have argued that m the procedural interpretation, operational semanttcs s proof theory and fixpoint semantics is model theory. From the logic programming point of view, any such system is a programming language. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on. The result of both the unfolding and the fixpoint semantics is a set of rrucriw hrkariors, which are trees abstractly representing all the possible. Wellfounded argumentation semantics for extended logic.

It does so by evaluating the meaning of syntactically valid strings defined by a specific programming language, showing the computation involved. Jan 01, 2007 read predicate introduction for logics with a fixpoint semantics. Wellfounded and stable semantics of logic programs with. The semantics of predicate logic as a programming language. The abstract interpretation foundations or the corresponding m2 course can also reveal interesting. The paper is a general overview of our approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semanticsbased program analysis. It is concluded that operational semantics is a part of proof theory and that fixpoint semantics is a special case of modeltheoretic semantics. Kowalskis procedural interpretation of logic, has not only procedurally interpreted horn clauses, but also limited the.