New semantic tools for logic programming springerlink. David bourget western ontario david chalmers anu, nyu area editors. In this chapter, we describe a fixpoint semantics for a knowledge base that is based on a multivalued logic. Probabilistic logic programming is at the intersection of two wider research. One source of this richness is the inherent nonmonotonicity of its negation. Toward a declarative semantics for infinite objects in logic. Series was designed to cover groups of books generally understood as such.
Once the classical semantics of logic programs have been introduced, the revision operator t p is defined, in order to present the aptvan emdenkowalski semantics. Fixpoint semantics for logic programming a survey core. Mechanizing programming logics in higher order logic. Author raphael finkel, university of kentucky, intersperses the discussion of these models with indepth coverage. Mathematical aspects of logic programming semantics crc. 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. This book is concerned with the second form when the underlying logic is higherorder logic. In a sense, this operator captures the modus ponens rule of inference. This paper presents a fixpoint semantics for fuzzy linguistic logic programs and based on it proves the completeness of the computational model.
Mathematical aspects of logic programming semantics crc press book 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. The semantics of predicate logic as a programming language. This paper describes a simpler way for programmers to reason about the correctness of their code. The fixpoint completion fix p of a normal logic program p is a program transformation such that the stable models of p are exactly the models of the clark completion of fix p. Such languages are similar to the sql database language. Pdf fixpoint semantics for logic programming a survey. To compute the truth value of a query, a computational model which directly manipulates linguistic terms is provided. Semantics and pragmatics 2 winter 2011 university of chicago handout 1 1 logic, language and meaning a formal system is a set of primitives, some statements about the primitives axioms, and some method of deriving further statements about the primitives from the axioms. Previous proposals for elp semantics can be divided into two classes. Fixpoint 3valued semantics for autoepistemic logic 3 to determine the truth value of a formula under our semantics is in the class. Since logic programming involves both logic and programming, it should not be surprising that several varieties of semantics have been developed for it. Computability theory, semantics, and logic programming.
It covers translation, proofs, and formal semantics for sentential and predicate logic. The book presents the main ideas for semantics, inference, and learning and. Predicate logic calculus is a formal system consisting of. This book gives an account oc the mathematical coundations oc logic programming. However, to reason about correctness and to add further features, it is useful to reinterpret the construction in a higherorder booleanvalued model involving a measure algebra. The gelfondlifschitz operator of p coincides with the immediate consequence operator of fix p, as. The only prerequisites are some camiliarity with a logic programming. 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. Fixpoint semantics and optimization of recursive datalog. Melvin fitting, the stable model semantics for logic. The stable model semantics for logic programming ut cs. Truszczynski, editors, logic programming and nonmonotonic reasoning, pages 143155.
A fixpoint semantics and an sldresolution calculus for modal logic programs linh anh nguyen institute of informatics university of warsaw ul. The author provides a homogeneous treatment of the semantics of both theoretical and practical logic programming languages. A fixpoint semantics and an sldresolution calculus for. Domain theory and fixpoint semantics, imperative programming. Foundations of probabilistic logic programming river publishers. Predicate introduction for logics with fixpoint semantics.
This is one of several standard approaches to the meaning of negation in logic programming, along. Logic programming has developed into a broad discipline within computing science, contributing to such fields as artificial intelligence, newgeneration computing, software engineering and deductive databases. They closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systemsneural networks. This disambiguation page lists articles associated with the title formal semantics.
The paper is a general overview of our approach to the semantics of logic programs. There are a few theoretical differences between these references and the contents. In the context of logic programming, dmt showed that fittings three or fourvalued immediate consequence operator is an approximator of the usual twovalued immediate consequence operator, and that the major semantics of logic programs coincide with the equally named different types of fixpoints of that approximator. Swiprolog theory and practice of logic programming. Melvin fitting, computability theory, semantics, and logic. Watt, 97807262663, available at book depository with free delivery worldwide. In nitegame semantics for logic programming languages. The semantics of predicat e logic as a programming language m. Mathematical aspects of logic programming semantics. Fixpoint semantics for logic programming a survey sciencedirect. This book describes computability theory and provides an extensive treatment of data structures and program correctness. Logic programming, fundamenta informaticae on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. 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.
This is wellknown and was studied by dung and kanchanasut 15. The remaining chapters of the book discusses alternative approaches to logic programming, such as using parallelism to solve subgoals simultaneously and its connection with concurrent logic programming. Programming, logic, and semantics group home people meetings resources. Constraint logic programming scheme, in 8 on prolog ii as a logic program ming language scheme, and in io, giving a logical semantics to a language without occur check containing both equations and inequations. Then we define a fixpoint semantics for prolog computed resultants, i. The fixpoint semantics is based on the immediate consequence operator which maps the set of facts in a cinterpretation to the set of facts which are implied by the rules in the program. We propose a modal logic programming language called mprolog, which is as expressive as the general modal horn fragment. The semantics of constraint logic programs sciencedirect. It generalises the traditional herbrand universe semantics, and specialises the semantics of logical relations, as used in analysing parametricity in functional and imperative programming languages.
Pdf the stable model semantics for logic programming. It covers syntax, semantics, and pragmatics of higher. Fixpoint semantics for logic programming a survey melvin fittinga. An effective fixpoint semantics for linear logic programs. According to a popular view on logic programming, the problem of the semantics was solved once and for all by logicians before logic programming was even born. This semantics, actually two semantics, are called fixpoint semantics and generalize the t p semantics for logic programs. Suitable abstractions of such a semantics are then used to model call patterns and partial answers. 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. On the semantics of negations in logic programming springerlink.
An application of the fixpoint operator can be computed algorithmically. Pdffront matter title page, acm books, contents, preface. Using these results on unfolding manyvaluedness, we then give manyvalued fixpoint characterizations for the set of all minimal models and the least model state. Section6discusses howpartialcorrectness speci cations canberegardedasabbre. Section 5 gives the semantics of the language described in section 2 and the semantics of hoarestyle partial correctness speci cations. I have attempted to make the book selccontained by including proocs of almost all the results needed. Fixpoint semantics and completeness of the computational model for fuzzy linguistic logic programming conference paper. Read predicate introduction for logics with a fixpoint semantics. It discusses applications to computational logic and.
The results in this tbesis apply to equational and constraint logic programming lan guages that a. The only prerequisites are some camiliarity with a logic programming language, such as prolog, and a certain. It significantly extends the tools and methods from tradi. Some people believe in a holy book, and their faith gives them the same feeling of certainty that sustains people of other faiths as well as nonbelievers. In this paper we summarize one variety of approaches to the semantics of logic programs. Check our section of free e books and guides on ml now. The concept of a stable model, or answer set, is used to define a declarative semantics for logic programs with negation as failure. For someone who comes to formalism from a programming background, the environmentbased semantics feels closer to what really happens with an expression that contains variables see also brians comment. Theory and practice of logic programming programming with. On prudent bravery and other abstractions, 1994, unpublished.
As stated in the introduction, only developments that have been of interest to the author are surveyed, but this is nevertheless a thorough and interesting presentation of the use of fixpoint theory in logic programming. The use of mathematical logic for computer programming. Many probabilistic logic programming plp semantics have. Fixpoint semantics for active integrity constraints. Dec 14, 2014 this describes my understanding of an approach to general semantics of logic programming that has been developed by marc denecker and his colleagues and students at leuven. The only prerequisites are some camiliarity with a logic programming language, such as prolog, and a certain mathematical maturity. This new book presents the fundamentals of logic programming from. Swiprolog is neither a commercial prolog system nor a purely academic enterprise, but increasingly a community project.
Objectives the main objective of both editions of this textbook is to provide a uniform account of both the foundations of logic programming and simple programming techniques in the programming. On the other hand, substitution seems to be how variables are usually explained in elementary mathematics education. Logic programming languages, of which prolog programming in logic is the best known, state a program as a set of logical relations e. The book covers topics spanning the period from the early days of logic programming to current times. Citeseerx a fibrational semantics for logic programs. Fixpoint semantics and completeness of the computational. First we use saturation to model the operational semantics of logic programs as coalgebrae on presheaves. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. Nonmonotonic logic is now seen as a close relative of logic programming, and developments in either area tend to a.
Jun 16, 2005 an extended logic program elp is a logic program that allows for classical negation as well as for negationasfailure. On greatest fixpoint semantics of logic programming. Syntax, semantics, and proof introduces students to the fundamental concepts, techniques, and topics involved in deductive reasoning. In particular, logic programming has contributed to the understanding of the semantics of a database, has extended the concept of relational databases, and has introduced new techniques in providing useful tools for database users. A notation will provide a way to represent two clearly different representations for two different meanings of a twoways ambiguous sentence. A fixpoint semantics and an sldresolution calculus for modal. Librarything has 2 suggested works for this series. We then use the fixpoint semantics to provide formal definitions for four types of knowledge base anomalies. Agler guides students through the basics of symbolic logic by explaining the essentials of two classical systems, propositional and predicate logic. Chapter 2 is concerned with the procedural semantics oc logic programs. As mentioned above, the semantics we propose can be applied to approx.
We first extend to resultants some classical results of logic programming theory. We introduce new notions and modify the classical semantics, i. Purely functional data structures by chris okasaki, functional programming in scala by runar bjarnason, learn yo. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional lo. We propose a new declarative semantics for logic programs with negation. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Scotland abstract sentences in firstorder predicate logic can be usefully interpreted as programs in this paper the. The semantics of predicate logic as a programming language m. A denotational semantics approach to functional and logic. The authors develop wellknown and important semantics in logic programming from a unified point of view using both order theory and new, nontraditional methods. The study of fixpoints has long been at the heart of logic programming.
The purpose of this article is to demonstrate the significant impact that logic programming has had on databases. 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. Free ml books download ebooks online textbooks tutorials. We give a fixpoint semantics and an sldresolution calculus for mprolog in all of the basic serial modal logics kd, t, kdb, b, kd. The concept of constraint programming was introduced in artificial intelligence and graphics in the 1960s and 1970s. 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. Thus, existing technology for classical disjunctive logic programming can be used to implement manyvalued disjunctive logic programming. We introduce a new semantics for logic programming languages. If an internal link led you here, you may wish to change the link to point directly to the intended article. A denotational semantics approach to functional and logic programming tr89030 august, 1989 frank s. Written for the student or professional interested in programming language design, this new book examines a wide range of programming language paradigms and issues.
A bossi, dipartimento di matematica pura ed applicata, universita di padova, via belzoni 7, i351 padova, italy. In nitegame semantics for logic programming languages chrysida galanaki. Researchers interested in logic programming or semantics, as well as artificial intelligence search strategies need to consult this book as the only source for some essential and new ideas in the area. We specify here the least model semantics, the fixpoint semantics, and an sldresolution calculus for modal logic programs in the multimodal logic kd4i g 5a, which is intended for reasoning about. Golson d a greatest fixed point characterization of the minimal infinite objects computed by a nonterminating logic program is presented, avoiding dif ficulties experienced by other attempts in the literature. Cristina david royal society university research fellow. An introduction to the stable and wellfounded semantics of logic programming 3. We develop the semantics of an extended stochastic calculus suitable for modeling a simple higherorder probabilistic programming language. It makes accessible some of the authors work on generalized recursion theory, particularly the material on the logic programming language prolog, which is currently of great interest. Citeseerx the stable model semantics for logic programming. A generic semantics for constraint functional logic programming. Constraint programming is like an octopus spreading its tentacles into databases, operations research, artificial intelligence, and many other areas. Mathematical aspects of logic programming semantics chapman. 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.
Resultants semantics for prolog, journal of logic and. Citeseerx fixpoint semantics for logic programming a. This section contains free e books and guides on ml, some of the resources in this section can be viewed online and some of them can be downloaded. This thesis focuses on the study of the semantics of logic programs and the development of in nite games of perfect information.
The computational model has been proved to be sound. Review much of the material has been generated by the authors own. Fixpoint semantics and completeness of the computational model for fuzzy linguistic logic programming. Fixpoint semantics and optimization of recursive datalog programs with aggregates. Buy computability theory, semantics, and logic programming oxford logic guides on free shipping on qualified orders. The study of semantics of logic programs has shown strong. The core system has been shaped to its current form while being used as a tool for building research prototypes, primarily for knowledgeintensive and interactive systems.
Now the related techniques are used and studied in many fields of computing. Oct 06, 2011 the development of logical notation for semantics is a result of the need to be able to talk about propositions and represent them in an unambiguous manner. Also discussed is how to associate functions with functors, in order to incorporate a notion of equality into logic programming. As such, it allows properties of these different semantics for all of these logics to be studied in a uniform way. The delineation between semantic and syntactic entailment is emphasised very much in most texts. In the second part, various logic programming based reasoning features are applied to model these identified morality viewpoints, via classic.