Expressiveness of answer set languages



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Answer set programming (ASP) is a form of declarative programming oriented towards difficult combinatorial search problems. It has been applied, for instance, to plan generation and product configuration problems in artificial intelligence and to graph-theoretic problems arising in VLSI design and in historical linguistics. Syntactically, ASP programs look like Prolog programs, but the computational mechanisms used in ASP are different: they are based on the ideas that have led to the development of fast satisfiability solvers for propositional logic. ASP is based on the answer set/stable model semantics for logic problems, originally intended as a specification for query answering in Prolog. From the original definition of 1988, the semantics was independently extended by different research groups to more expressive kinds of programs, with syntax and semantics that are incompatible with each other. In this thesis we study how the various extensions are related to each other. In order to do that, we propose another definition of an answer set. This definition has three main characteristics: (i) it is very simple, (ii) its syntax is more general than the usual concept of a logic program, and (iii) strong theoretical tools can be used to reason on it. About (ii), we show that our syntax allows constructs defined in many other extensions of the answer sets semantics. This fact, together with (iii), allows us to study the expressiveness of those constructs. We also compare the answer set semantics with another important formalism developed by Norm McCain and Hudson Turner, called logic.