This paper outlines a novel approach to the computation of answer sets in an evolving and interactive environment. Instead of recomputing the semantics of the entire program, our approach updates the answer sets after incremental changes to the rule base. This is intended for application domains in which the answer set program is developed or updated during the run time of the system but answer sets are required throughout. In this paper we focus on the theoretical background and presentation of the algorithm for handling the addition.
ID-logic uses ideas from the field of logic programming to extend second order logic with non-monotone inductive defintions. In this work, we reformulate the semantics of this logic in terms of approximation theory, an algebraic theory which generalizes the semantics of several non-monotonic reasoning formalisms. This allows us to apply certain abstract modularity theorems, developed within the framework of approximation theory, to ID-logic. As such, we are able to offer elegant and simple proofs of generalizations of known theorems, as well as some new results.
Possibilistic Stable model Semantics is an extension of Stable Model Semantics that allows to merge uncertain and non monotonic reasoning into a unique framework. To achieve this aim, knowledge is represented by a normal logic program where each rule is given with its own degree of certainty. By this way, it formally defines a distribution of possibility over atom sets that, on its turn, induces for each atom a possibility and a necessity measures. The latter underpins the definition of a possibilistic stable model in which every consequence of the program is given with a level of certainty. In this work we explain how we can compute the possibilistic stable models of a possibilistic normal logic program by using available softwares for Answer Set Programming and we describe the main lines of the system that we have developed.
In this paper we consider an extension of the answer set semantics allowing arbitrary use of strong negation. We prove that the strong negation extension of any intermediate logic provides a suitable basis for reasoning under the answer set semantics. We propose two new notions of equivalence that are more general than strong equivalence: substitution equivalence and contextualized equivalence.
In this paper we develop a declarative language for modular answer set programming (ASP). Our language allows to declaratively state how one ASP module can import processed answer sets from another ASP module. We define the syntax and semantics of our language and illustrate its applicability by modeling the ACC tournament scheduling problem. Besides the elegance of developing declarative programs in a modular manner, our illustration shows that a problem that is not timely solvable when done in a monolithic way, but becomes solvable when done in a modular way.
This paper discusses the background, algorithms and implementation techniques to support programmers in 'debugging' logic programs under the answer set semantics. We first investigate what constitutes an error in such programs and which classes of errors exist. This is used to motivate techniques and algorithms that respectively eliminate certain classes of errors and explain how an error occurred and why it occurred. Finally, details of the IDEAS (Interactive Development and Evaluation tool for Answer Set Semantics) system are given, a prototype version of which implements all of the techniques described.
The extended answer set semantics for simple logic programs, i.e. programs with only classical negation, allows for the defeat of rules to resolve contradictions. In addition, a partial order relation on the program’s rules can be used to deduce a preference relation on its extended answer sets. In this paper, we propose a “quantitative” preference relation that associates a weight with each rule in a program. Intuitively, these weights define the “cost” of defeating a rule. An extended answer set is preferred if it minimizes the sum of the weights of its defeated rules. We characterize the expressiveness of the resulting semantics and show how the semantics can be conveniently extended to sequences of weight preferences, without increasing the expressiveness. We illustrate an application of the approach by showing how it can elegantly express largest common subgraph and subgraph isomorphic approximation problems, a concept often used in intelligence analysis to find similarities or specific regions of interest in large graphs of observed activity.
Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for finding answer sets for disjunctive logic programs. We implement two different ways of SAT solver invocation used in nondisjunctive answer set programming. The algorithms are based on the definition of completion for disjunctive programs and the extension of loop formula to the disjunctive case. We propose the necessary modifications to the algorithms known for nondisjunctive programs in order to adapt them to the disjunctive case and demonstrate their implementation based on system CMODELS.
Despite all efforts on intelligent grounding, state-of-the-art answer set solvers still have huge memory requirements, because they compute the ground instantiation of the input program before the actual reasoning starts. This prevents ASP to be effective on several classes of problems. In this paper we integrate answer set generation and constraint solving to reduce the memory requirements for a class of multi-sorted logic programs with cardinality constraints. We prove some theoretical results, introduce a provably sound and complete algorithm, and report experimental results showing that our approach can solve problem instances with significantly larger domains.
Answer Set Programming (ASP) and propositional satisfiability (SAT) are closely related. In some recent work we have shown that, on a wide set of logic programs called “tight”, the main search procedures used by ASP and SAT systems are equivalent, i.e., that they explore search trees with the same branching nodes. In this paper, we focus on the experimental evaluation of different search strategies, heuristics and their combinations that have been shown to be effective in the SAT community, in ASP systems. Our results show that, despite the strong link between ASP and SAT, it is not always the case that search strategies, heuristics and/or their combinations that currently dominate in SAT are also bound to dominate in ASP. We provide a detailed experimental evaluation for this phenomenon and we shed light on future development of efficient Answer Set solvers.
In previous work, action languages have predominantly been concerned with domains in which values are static unless changed by an action. Real domains, however, often contain values that are in constant change. In this paper we introduce an action language for modeling such hybrid domains called the process description language. We discuss the syntax and semantics of the language, model an example using this language, and give a provenly correct translation into answer set programming.
