We show that ground logic programs can be modelled by either p f p fcoalgebras or p f listcoalgebras on. 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. In particular, we discuss complete derivation systems. A simple illustration of this procedure might be useful. 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. Citeseerx document details isaac councill, lee giles, pradeep teregowda. As a special theme, alcop 2015 will explore connections with substructural logics and their applications in computer science, social science and ai e. In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. Pdf coalgebraic semantics for derivations in logic programming. Every variablefree logic program induces a p f p fcoalgebra on the set of atomic formulae in the program. A coalgebraic perspective on probabilistic 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.
We are trying to make language mechanisms which behave like thought. For example, the modal logic s4 is characterized by the class of topological boolean algebrasthat is, boolean algebras with an interior operator. Every variablefree logic program induces a p fp fcoalgebra on the set of atomic formulae in the program. In this paper, we give a coalgebraic semantics to logic programming. Moreover, for inductive relation symbols their interpretation in m needs to be forward closed under. International conference on algebra and coalgebra in computer science. Algebraic logic functional programming language wikipedia. Coalgebraic derivations in logic programming heriotwatt. In particular, we show that recently introduced coalgebraic logic programming 17 is. Coalgebra may be used to provide semantics for sldderivations, both finite and infinite. This cited by count includes citations to the following articles in scholar.
Coalgebraic semantics for derivations in logic programming. As an alternative to the lax approach of the above line of research, we propose saturation which, in the case of logic programming. It is the aim of coalgebraic modal logic to create a general framework for. Introduction to logic lecture 2 syntax and semantics of. 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. 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. Productive corecursion in logic programming theory and.
Separate chapters cover the intuitive logical semantics of the language, the powerful programming techniques supported by it and their connections. The design and study of such formal systems is the primary motivation of the. Syntax, semantics, and structuralism, i remember that there are two different meanings of undecidable. Lecture notes on mathematical logic university of texas. N1 computer science logic, 25th international workshop 20th annual conference of the eacsl, csl 2011, september 1215, 2011, bergen, norway. The coalgebra p sends an atomic formula ato the set. N2 coalgebra may be used to provide semantics for sldderivations, both finite and infinite. Coalgebraic semantics for parallel derivation strategies. Then, based upon coalgebraic semantics, we propose a new sound and complete algorithm for parallel derivations. 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. Pdf every variablefree logic program induces a p f p f coalgebra on the set of atomic formulae in the program. Equational logic as a programming language the mit press. Introduction inwhatfollowsilookatsomeformallanguagesthataremuch simplerthanenglishanddesnevalidity of arguments,truth underaninterpretation,consistency etc.
We are trying to catch some aspects of the action of intelligence within formal systems. A refutation subtree called success subtree in 31 is a finite derivation subtree with only. Scotland abstract sentences in firstorder predicate logic can be usefully interpreted as programs in this paper the. That correspondence has been developed to model firstorder programs in two ways, with lax semantics and saturated. A propositional logic program p may be identified with a p f p fcoalgebra on the set of atomic propositions in the program. Saturated semantics for coalgebraic logic programming. Pdf coalgebraic semantics for derivations in logic. A logic program is productive if it can give rise to productive derivations. Coalgebraic semantics for derivations in logic programming ekaterina komendantskaya1 and john power2 1 department of computing, university of dundee, uk. We propose a new declarative semantics for logic programs with negation.
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. The basic idea underlying the method of formal derivations is the following fundamental idea. Such definitions give rise to questions of lazy corecursive derivations and parallelism, as execution of such logic programs can have both. Introduction to logic lecture 2 syntax and semantics of propositional logic. Katya amast2010 coalgebraic semantics for parallel derivation strategies in logic programming. Logic programming supports recursive computations and some logic. A generic semantics for constraint functional logic.
Attendance is free of cost, but talks are by invitation only. In 21, we extended our analysis from variablefree logic programs to arbitrary logic programs. Thus, we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. 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. Such definitions give rise to questions of lazy corecursive derivations. Exploiting parallelism in coalgebraic logic programming. 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. We propose a method that semidecides productivity of individual derivations for regular formulae. Citeseerx the stable model semantics for logic programming. Algebraic logic functional programming language, also known as alf, is a programming language which combines functional and logic programming techniques.
John power, department of computer science, university of bath, bath ba27ay, uk. Modal logic, coalgebraic semantics, knowledge representation. Languages and programming icalp 2012, part ii, volume 7392 of. Logic programming, coalgebra, observational semantics, corecursion.
The second interpretation recovers the usual distribution semantics of plp. The practical converse, unfortunately, is also true. Our semantics naturally extends coalgebraic modal logic in that it is parametrized. Buy computability theory, semantics, and logic programming oxford logic guides on free shipping on qualified orders. Bialgebraic semantics for logic programming 3 a natural transformation in setc and, consequently, the abstract semantics results to be compositional. We first give such semantics to classical sldderivations, proving results such as adequacy, soundness and completeness. Ekaterina komendantskaya, joint work with john power and guy mccusker th international conference on algebraic methodology and software technology amast10, 24 june 2010. Coalgebraic semantics for parallel derivation strategies in logic programming.
Logic programming, sldresolution, coalgebra, lawvere theories, lax natural transformations, oplax maps of coalgebras. Semantics, algebras, and derivation systems on free shipping on qualified orders. The semantics of predicate logic as a programming language. 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.
The semantics of predicate logic as a programming language m. Computability theory, semantics, and logic programming. An algebraic framework for the definition of compositional. An introduction to manyvalued and fuzzy logic book. Anyone who hasnt already mastered sentential logic derivations will have tremendous difficulty with predicate logic derivations. 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. Lecture notes on mathematical logic vladimir lifschitz january 16, 2009 these notes provide an elementary, but mathematically solid, introduction to propositional and. Logic programming supports recursive computations, and some logic programs resemble the inductive or coinductive definitions written in functional programming languages.
In this paper, we extend that analysis to arbitrary logic programs. 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. 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. 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. Granting the validity of a few selected argument forms, we can demonstrate the validity of other argument forms. 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. Other modal logics are characterized by various other algebras with operators.