What is answer set programming to propositional satisfiability

Propositional satisfiability (or satisfiability) and answer set programming are two closely related subareas of Artificial Intelligence that are used to model and solve difficult combinatorial search problems. Satisfiability solvers and answer set solvers are the software systems that find satisfying interpretations and answer sets for given propositional formulas and logic programs, respectively. These systems are closely related in their common design patterns. In satisfiability, a propositional formula is used to encode problem specifications in a way that its satisfying interpretations correspond to the solutions of the problem. To find solutions to a problem it is then sufficient to use a satisfiability solver on a corresponding formula. Niemelä, Marek, and Truszczyński coined answer set programming paradigm in 1999: in this paradigm a logic program encodes problem specifications in a way that the answer sets of a logic program represent the solutions of the problem. As a result, to find solutions to a problem it is sufficient to use an answer set solver on a corresponding program. These parallels that we just draw between paradigms naturally bring up a question: what is a fundamental difference between the two? This paper takes a close look at this question

Logic Programming for Describing and Solving Planning Problems

A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm, all program rules are considered as constraints and solutions are stable models of the rule set. This is a rather radical departure from the standard paradigm of logic programming. In this paper we revisit abductive logic programming and argue that it allows a programming style which is as declarative as programming based on stable models. However, within abductive logic programming, one has two kinds of rules. On the one hand predicate definitions (which may depend on the abducibles) which are nothing else than standard logic programs (with their non-monotonic semantics when containing with negation); on the other hand rules which constrain the models for the abducibles. In this sense abductive logic programming is a smooth extension of the standard paradigm of logic programming, not a radical departure.Comment: 8 pages, no figures, Eighth International Workshop on Nonmonotonic Reasoning, special track on Representing Actions and Plannin

Logic Programming Approaches for Representing and Solving Constraint Satisfaction Problems: A Comparison

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the variables of the constraint satisfaction problem. On the other hand there are systems based on stable model semantics, abductive systems, and first order logic model generators which compute solutions as models of some theory. This paper compares these different approaches from the point of view of knowledge representation (how declarative are the programs) and from the point of view of performance (how good are they at solving typical problems).Comment: 15 pages, 3 eps-figure

Formal Concept Analysis and Resolution in Algebraic Domains

We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis. The results shed light on the use of contexts and domains for knowledge representation and reasoning purposes.Comment: 14 pages. We have rewritten the old version according to the suggestions of some referees. The results are the same. The presentation is completely differen

An Integrated Development Environment for Declarative Multi-Paradigm Programming

In this paper we present CIDER (Curry Integrated Development EnviRonment), an analysis and programming environment for the declarative multi-paradigm language Curry. CIDER is a graphical environment to support the development of Curry programs by providing integrated tools for the analysis and visualization of programs. CIDER is completely implemented in Curry using libraries for GUI programming (based on Tcl/Tk) and meta-programming. An important aspect of our environment is the possible adaptation of the development environment to other declarative source languages (e.g., Prolog or Haskell) and the extensibility w.r.t. new analysis methods. To support the latter feature, the lazy evaluation strategy of the underlying implementation language Curry becomes quite useful.Comment: In A. Kusalik (ed), proceedings of the Eleventh International Workshop on Logic Programming Environments (WLPE'01), December 1, 2001, Paphos, Cyprus. cs.PL/011104