Fixpoint semantics for logic programs cs240b notes notes based on section 8. Several alternative semantics have been put forward, exposing operational details of the computation state. My guess would be model theory since the fixpoint semantics of a logic program is its model. Citeseerx program transformation for program verification. In this paper, we study predicate introduction in the algebraic framework of approximation theory. Unfolding is also used to define an immediate consequences operator and, therefore, a fixpoint semantics in the typical logic programming style. Second international conference, nancy, france, october, 1990. In this paper, a logic program under the stable semantics is constructed to capture the meaning of theories in the action language al. The analysis and verification of software systems is an important issue. Semantics of logic synonyms, semantics of logic pronunciation, semantics of logic translation, english dictionary definition of semantics of logic. Fixpoint 3valued semantics for autoepistemic logic 3 to determine the truth value of a formula under our semantics is in the class.
Semantics of programming languages exposes the basic motivations and philosophy underlying the applications of semantic techniques in computer science. Alternating fixpoint theory for logic programs with priority. However, it has also another important application. A fixpoint semantics for disjunctive logic programs sciencedirect. It is concluded that operational semantics is a part of proof theory and that fixpoint semantics is a special case of modeltheoretic semantics. Fixpoint semantics and optimization of recursive datalog.
It may be threevalued in the sense that for a subclass of formulas. A survey of semantic description frameworks for programming. The latter fact led to the development of a functional or fixedpoint semantics for logic programs with which we are concerned in this. Approximation fixpoint theory and the semantics of logic. Study the syntax and semantics of integer type declarations, the evaluation of integer arithmetic expressions, the evaluation of boolean expressions and the execution of assignments, tests and iterations for the c programming language either in the 1975 c reference manual by brian w. The least fixpoint semantics and negation allow us to denote both the least models and the greatest models of programs, and thus to reason about the finite or infinite behaviour of programs. Unfolding and fixpoint semantics of concurrent constraint.
The advantages of our framework in comparison to previous tools along this line of research are its easy, userfriendly syntax, and its expressivity through the availability of default. Pdf fixpoint semantics for logic programming a survey. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. The goal of this work is to develop the least model semantics, a xpoint semantics, and an sldresolution calculus, in a \direct way and closely to the style of classical logic programming, this is a revised version of \l. Interested in program synthesis, software verification, especially the verification of heapmanipulating programs, program termination and the design of decision procedures. It does so by evaluating the meaning of syntactically valid strings defined by a specific programming language, showing the computation involved. Theoretical foundations and semantics of logic programming. Semantics and verification of software informatik 2.
Knowledge compilation of logic programs using approximation. Fixpoint and modeltheoretic semantics of logic programs with respect to herbrand interpretations generalize to these semantics for relational programs with respect to finterpretations. Fixpoint semantics for logic programming a survey request pdf. Syntax, semantics and implementation details of a simple and expressive fuzzy tool over prolog. Designed as a text for upperlevel and graduatelevel students, the mathematically sophisticated approach will also. Kowalskis procedural interpretation of logic, has not only procedurally interpreted horn clauses, but also limited the. This fixpoint characterizes a unique but possibly threevalued belief set of an autoepistemic theory. Fixedpoint semantics for definitional higherorder logic programs. The idea of semantics is that the linguistic representations or symbols support logical outcomes, as a set of words and. 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. Aug 01, 2005 the study of semantics of logic programs has shown strong links between the model theoretic semantics truth and falsity of atoms in the programmers interpretation of a program, procedural semantics for example, sld resolution and fixpoint semantics which is useful for program analysis and alternative execution mechanisms. Inoue and sakama 1996 developed a fixpoint semantics for abductive logic programs in which the belief models are characterized as the fixpoint of a disjunctive program obtained by a suitable program transformation.
Semantics of logic definition of semantics of logic by. 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. We use examples and describe the semantics operationally. Since logic programming involves both logic and programming, it should not be surprising that several varieties of semantics have been developed for it. Education software downloads ladder logic simulator by triangle research international, inc and many more programs are.
Finding program bugs is a longstanding problem in software construction. Papers in semantics theory of programming and artificial. Foundations of deductive databases and logic programming, morgan. Logic program composition operator logic programming partial answer abstract. In our case, the input term can be reduced in the semantics by using standard term. The paper presents a constructive 3valued semantics for autoepistemic logic ael. Prologs very useful expressive power is not captured by traditional logic programming semantics, due mainly to the cut and goal and clause order. Ritchie or in the 1999 standard definition of the c programming language.
The study of semantics of logic programs has shown strong links between the model theoretic semantics truth and falsity of atoms in the programmers interpretation of a program, procedural semantics for example, sld resolution and fixpoint semantics which is useful for program analysis and alternative execution mechanisms. An effective fixpoint semantics for linear logic programs. However, we know that coincides with for logic programs, so the semantics based on proving resolution coincide with the semantics based on the fixed points models. In logic, the semantics of logic is the study of the semantics, or interpretations, of formal and idealizations of natural languages usually trying to capture the pretheoretic notion of entailment overview.
In such a case that the evaluation would be of syntactically invalid strings, the result would be non. It introduces the mathematical theory of programming languages with an emphasis on higherorder functions and type systems. Approximation fixpoint theory and the semantics of logic and. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested. A new fixpoint semantics for general logic programs compared. In this approach we describe the formal syntax, the operational semantics and the declarative semantics of rfuzzy based on a lattice. An excellent survey of fixpoint semantics for logic programming is fit99. It significantly extends the tools and methods from traditional order theory to include nonconventional. Scotland abstract sentences in firstorder predicate logic can be usefully interpreted as programs in this paper the. In particular, safetycritical systems are ones in which errors can be disastrous. 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.
Semantics in it is a term for the ways that data and commands are presented. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional lo. Fixpoint semantics for logic programming a survey sciencedirect. We present the rfuzzy framework, a prologbased tool for representing and reasoning with fuzzy information. Our construction is intermediate between van gelders wellfounded model and gelfond and lifschitzs stable model semantics. We present a fixpoint semantics for disjunctive logic programs. Equivalence of two fixedpoint semantics for definitional higher.
Predicate introduction for logics with a fixpoint semantics. In other words, we have to learn more from computer science than from mathematical logic. Abstract in this paper we discuss a new semantic characterization of inheritance in logic programming. Our approach is inspired both by existing literature on denotational. Techniques to safeguard against such scenarios are essential for such systems. A new fixpoint semantics for general logic programs. In our semantics, the meaning of a program is, as in the classical case, the. We study a new fixpoint semantics for logic programs with negation. 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. Download ladder logic programming software for free windows. The study of semantics of logic programs has shown strong links between. Clarks predicate completion is defined for logic programs with negation.
This paper clarifies how this fixpoint theory can define the stable. The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of. Programming, logic, and semantics group home people meetings resources. Then, a denotational semantics of the equivalent, propositional, and infinite dlp program groundp, provides a. Mar 24, 2020 semantics is the study of meaning conveyed by linguistic structures.
Abstract interpretation using advanced logic programming. We show first that the stable models of a logic programp are exactly the wellsupported models ofp, i. A fixpoint semantics and an sldresolution calculus for modal logic programs. A natural semantics for logic programs with negation. The semantics of predicate logic as a programming language m. Fixpoint semantics and optimization of recursive datalog programs with aggregates. 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. It is differentiated from the lexical which determines what is or isnt a valid word or symbol in the language and the syntactic provider of rules to combine those words or sy. For definite clause programs these different semantics are all equivalent. Reliable semantics for extended logic programs with rule prioritization. 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 kripkekleene semantics for logic programs, journal of logic programming, 24, 1985, 295312. The language of non deterministic logic programs framework is extended with nonmonotonic negation, and two. A compact fixpoint semantics for term rewriting systems.
Nonmonotonic logic is now seen as a close relative of logic programming, and developments in either area tend to a. Cristina david royal society university research fellow. As usual for declarative programs, the engine might actually choose a very different way of computing the model. Sld resolution and fixpoint semantics which is useful for program. Moreover, in deductive databases it is usual to split a logic program p into idb rules. 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. Minimum model semantics for logic programs with negationas. In this post, i use the term stratified partial fixpoint semantics as the name of the semantics used by the logiql 4. In this paper we summarize one variety of approaches to the semantics of logic programs. In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages. Download ladder logic programming software for free. A fixpoint semantics and an sldresolution calculus for modal.
Citeseerx fixpoint semantics for logic programming a. A compositional semantics for logic programs 5 derivable atoms. Minimal models and fixpoint semantics for definite logic programs. An application of the fixpoint operator can be computed algorithmically. The paper presents a constructive fixpoint semantics for autoepistemic logic ael. A fixed point semantics is developed for logic programming, allowing any. They show that abductive logic programming is related to the justificationbased truth maintenance system of doyle 1979. Semantics is the study of meaning conveyed by linguistic structures. We extend the concept of the herbrand base of a logic program to consist of all positive clauses. The unfolding semantics is obtained as a limit of an infinite unfolding process. On greatest fixpoint semantics of logic programming. The idea of such a semantics seems clearcut, as already demonstrated by several works in other programming paradigms like logic programming 8, 18. The fixpoint theory does not apply to general programs with negation. A least model semantics, a least fixpoint semantics and an operational semantics are introduced and their equivalence is proven.
As mentioned above, the semantics we propose can be applied to approximate the skeptical mode of autoepistemic reasoning. The study of fixpoints has long been at the heart of logic programming. We provide a real implementation that is free and available. This paper clarifies how this fixpoint theory can define the stable and wellfounded semantics of logic programs. Semantics is a linguistic concept separate from the concept of syntax, which is also often related to attributes of computer programming languages. The semantics of predicate logic as a programming language. The semantics is 3valued in the sense that, for some formulas, the least fixpoint does not specify whether they are believed or not. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical. However, this would lead us nowhere, since the equivalence we need must be based on the operational behavior and on what we can observe from a computation. In general, it fails to capture their intended semantics 7,8,9. A fixpoint semantics and an sldresolution calculus for. In particular, static causal laws of the following form are considered.
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