Coalgebraic semantics for derivations in logic programming pdf

A logic program is productive if it can give rise to productive derivations. Then, based upon coalgebraic semantics, we propose a new sound and complete algorithm for parallel derivations. Lecture notes on mathematical logic university of texas. In 21, we extended our analysis from variablefree logic programs to arbitrary logic programs. Equational logic as a programming language the mit press. A propositional logic program p may be identified with a p f p fcoalgebra on the set of atomic propositions in the program. The corresponding c p f p fcoalgebra, where c p f p f is the cofree comonad on p f p f, describes derivations by resolution.

Coalgebraic derivations in logic programming heriotwatt. We propose a new declarative semantics for logic programs with negation. Anything that you see talking about undecidability of a class of problems is almost surely talking about the computability meaning, which as weve said several times is distinct from the logical one, which is the one in use here. For example, the modal logic s4 is characterized by the class of topological boolean algebrasthat is, boolean algebras with an interior operator.

In particular, we discuss complete derivation systems. Our starting point is the key observation that, in coalgebraic logic programming 30 32 31 33, the operational semantics fails to be a natural transformation. A simple illustration of this procedure might be useful. The design and study of such formal systems is the primary motivation of the. An introduction to manyvalued and fuzzy logic book. The coalgebra p sends an atomic formula ato the set. An algebraic framework for the definition of compositional. In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. N2 coalgebra may be used to provide semantics for sldderivations, both finite and infinite. We are trying to catch some aspects of the action of intelligence within formal systems. Every variablefree logic program induces a p f p fcoalgebra on the set of atomic formulae in the program.

Coalgebraic semantics for parallel derivation strategies. Coalgebraic semantics for derivations in logic programming ekaterina komendantskaya1 and john power2 1 department of computing, university of dundee, uk. In this paper, we give a coalgebraic semantics to logic programming. A refutation subtree called success subtree in 31 is a finite derivation subtree with only. Association for logic programming alp the association for logic programming alp was founded in 1986, with the mission to contribute to the development of logic programming, relate it to other formal and also to humanistic sciences, and to promote its uses in academia and industry all over the world. Katya amast2010 coalgebraic semantics for parallel derivation strategies in logic programming. Equational logic as a programming language covers the entire spectrum of theoretical and applied work involved in eight years of designing and implementing the equational logic programming language. Every variablefree logic program induces a p fp fcoalgebra on the set of atomic formulae in the program. Algebraic logic functional programming language wikipedia. Logic has come to occupy a central position in the repertory of technical knowledge, and various types of logic started playing a key roles in the modelling of reasoning. Coalgebra may be used to provide semantics for sldderivations, both finite and infinite.

Syntax, semantics, and structuralism, i remember that there are two different meanings of undecidable. Thus, we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. Introduction to logic lecture 2 syntax and semantics of. The basic idea underlying the method of formal derivations is the following fundamental idea. Semantics, algebras, and derivation systems on free shipping on qualified orders. Algebraic logic functional programming language, also known as alf, is a programming language which combines functional and logic programming techniques. In this paper, we extend that analysis to arbitrary logic programs. It is the aim of coalgebraic modal logic to create a general framework for. A generic semantics for constraint functional logic.

Scotland abstract sentences in firstorder predicate logic can be usefully interpreted as programs in this paper the. We propose a method that semidecides productivity of individual derivations for regular formulae. Pdf coalgebraic semantics for derivations in logic programming. Katya arw11 coalgebraic derivations in logic programming arw 11 3 24 in one slide, it is the sory of how one started with looking for a suitable semantics. A coalgebraic perspective on probabilistic logic programming. Our semantics naturally extends coalgebraic modal logic in that it is parametrized. Computability theory, semantics, and logic programming. That correspondence has been developed to model firstorder programs in two ways, with lax semantics and saturated. As a special theme, alcop 2015 will explore connections with substructural logics and their applications in computer science, social science and ai e. John power, department of computer science, university of bath, bath ba27ay, uk. In particular, we show that recently introduced coalgebraic logic programming 17 is a paradigm in which, in contrast to many other alternative systems, the aspects of logic and control are. Lecture notes on mathematical logic vladimir lifschitz january 16, 2009 these notes provide an elementary, but mathematically solid, introduction to propositional and.

Its foundation is horn clause logic with equality which consists of predicates and horn clauses for logic programming, and functions and equations for functional programming alf was designed to be genuine. Languages and programming icalp 2012, part ii, volume 7392 of. In particular, we show that recently introduced coalgebraic logic programming 17 is. Logic programming, sldresolution, coalgebra, lawvere theories, lax natural transformations, oplax maps of coalgebras. The practical converse, unfortunately, is also true. Coalgebraic semantics for parallel derivation strategies in logic programming. Pdf every variablefree logic program induces a p f p f coalgebra on the set of atomic formulae in the program. Introduction to logic lecture 2 syntax and semantics of propositional logic. Ekaterina komendantskaya, joint work with john power and guy mccusker th international conference on algebraic methodology and software technology amast10, 24 june 2010. The second interpretation recovers the usual distribution semantics of plp. Such definitions give rise to questions of lazy corecursive derivations and parallelism, as execution of such logic programs can have both. Introduction inwhatfollowsilookatsomeformallanguagesthataremuch simplerthanenglishanddesnevalidity of arguments,truth underaninterpretation,consistency etc. Bialgebraic semantics for logic programming 3 a natural transformation in setc and, consequently, the abstract semantics results to be compositional. Modal logic, coalgebraic semantics, knowledge representation.

This book constitutes the refereed proceedings of the 4th international conference on algebra and coalgebra in computer science, calco 2011, held in winchester, uk, in augustseptember 2011. Citeseerx the stable model semantics for logic programming. Logic programming, coalgebra, observational semantics, corecursion. Separate chapters cover the intuitive logical semantics of the language, the powerful programming techniques supported by it and their connections. In an earlier paper, we identified a variablefree logic program with a p f p fcoalgebra on set and showed that, if c p f p f is the cofree comonad on p f p f, then given a logic program p qua p f p fcoalgebra, the corresponding c p f p f coalgebra structure describes the parallel andor derivation trees of p.

Citeseerx document details isaac councill, lee giles, pradeep teregowda. Such definitions give rise to questions of lazy corecursive derivations. Moreover, for inductive relation symbols their interpretation in m needs to be forward closed under. We are trying to make language mechanisms which behave like thought. As an alternative to the lax approach of the above line of research, we propose saturation which, in the case of logic programming. The semantics of predicate logic as a programming language. This cited by count includes citations to the following articles in scholar. Buy computability theory, semantics, and logic programming oxford logic guides on free shipping on qualified orders. Amast10 8 33 coalgebraic analysis of logic programs generally, given a functor f, an fcoalgebra is a pair s.

International conference on algebra and coalgebra in computer science. Exploiting parallelism in coalgebraic logic programming. N1 computer science logic, 25th international workshop 20th annual conference of the eacsl, csl 2011, september 1215, 2011, bergen, norway. Coalgebraic semantics for derivations in logic programming. Attendance is free of cost, but talks are by invitation only. We first give such semantics to classical sldderivations, proving results such as adequacy, soundness and completeness.

As we show in section 3, the algebraic semantics for logic programming 2,6,17 fails to give an account of the possibly in nite derivations that arise in the practice of logic programming. The semantics of predicate logic as a programming language m. Saturated semantics for coalgebraic logic programming. Other modal logics are characterized by various other algebras with operators. We show that ground logic programs can be modelled by either p f p fcoalgebras or p f listcoalgebras on. Anyone who hasnt already mastered sentential logic derivations will have tremendous difficulty with predicate logic derivations. 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.

For any set at, there is a bijection between the set of variablefree logic programs over the set of atoms at and the set of p fp fcoalgebra structures on at, where p f is the nite powerset functor on set. Logic programming supports recursive computations, and some logic programs resemble the inductive or coinductive definitions written in functional programming languages. Logic programming supports recursive computations and some logic. Pdf coalgebraic semantics for derivations in logic. Coalgebraic logic programming coalp we introduce in later sections uses a variety of treestructures both for giving semantics to logic programming and for implementation of coalp. Granting the validity of a few selected argument forms, we can demonstrate the validity of other argument forms.