A Tarskian Informal Semantics for Answer Set Programming

In their seminal papers on stable model semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational agent. To the best of our knowledge, theirs is still the only published systematic account of the intuitive meaning of rules and programs under the stable semantics. In current ASP practice, however, we find numerous applications in which rational agents no longer seem to play any role. Therefore, we propose here an alternative explanation of the intuitive meaning of ASP programs, in which they are not viewed as statements about an agent\u27s beliefs, but as objective statements about the world. We argue that this view is more natural for a large part of current ASP practice, in particular the so-called Generate-Define-Test programs

Arithmetic and Modularity in Declarative Languages for Knowledge Representation

The past decade has witnessed the development of many important declarative languages for knowledge representation and reasoning such as answer set programming (ASP) languages and languages that extend first-order logic. Also, since these languages depend on background solvers, the recent advancements in the efficiency of solvers has positively affected the usability of such languages. This thesis studies extensions of knowledge representation (KR) languages with arithmetical operators and methods to combine different KR languages. With respect to arithmetic in declarative KR languages, we show that existing KR languages suffer from a huge disparity between their expressiveness and their computational power. Therefore, we develop an ideal KR language that captures the complexity class NP for arithmetical search problems and guarantees universality and efficiency for solving such problems. Moreover, we introduce a framework to language-independently combine modules from different KR languages. We study complexity and expressiveness of our framework and develop algorithms to solve modular systems. We define two semantics for modular systems based on (1) a model-theoretical view and (2) an operational view on modular systems. We prove that our two semantics coincide and also develop mechanisms to approximate answers to modular systems using the operational view. We augment our algorithm these approximation mechanisms to speed up the process of solving modular system. We further generalize our modular framework with supported model semantics that disallows self-justifying models. We show that supported model semantics generalizes our two previous model-theoretical and operational semantics. We compare and contrast the expressiveness of our framework under supported model semantics with another framework for interlinking knowledge bases, i.e., multi-context systems, and prove that supported model semantics generalizes and unifies different semantics of multi-context systems. Motivated by the wide expressiveness of supported models, we also define a new supported equilibrium semantics for multi-context systems and show that supported equilibrium semantics generalizes previous semantics for multi-context systems. Furthermore, we also define supported semantics for propositional programs and show that supported model semnatics generalizes the acclaimed stable model semantics and extends the two celebrated properties of rationality and minimality of intended models beyond the scope of logic programs

Extending the Finite Domain Solver of GNU Prolog

International audienceThis paper describes three significant extensions for the Finite Domain solver of GNU Prolog. First, the solver now supports negative integers. Second, the solver detects and prevents integer overflows from occurring. Third, the internal representation of sparse domains has been redesigned to overcome its current limitations. The preliminary performance evaluation shows a limited slowdown factor with respect to the initial solver. This factor is widely counterbalanced by the new possibilities and the robustness of the solver. Furthermore these results are preliminary and we propose some directions to limit this overhead

Enfragmo: A system for modelling and solving search problems with logic

Abstract. In this paper, we present the Enfragmo system for specifying and solving combinatorial search problems. It supports natural specification of problems by providing users with a rich language, based on an extension of first order logic. Enfragmo takes as input a problem specification and a problem instance and produces a propositional CNF formula representing solutions to the instance, which is sent to a SAT solver. Because the specification language is high level, Enfragmo provides combinatorial problem solving capability to users without expertise in use of SAT solvers or algorithms for solving combinatorial problems. Here, we describe the specification language and implementation of Enfragmo, and give experimental evidence that its performance is comparable to that of related systems

Solving model expansion tasks: System design and modularity

In this thesis, we present the Enfragmo system for representing and solving combinatorial search problems. The system supports natural specification of problems by providing users with a rich language, based on an extension of first order logic. Since the specification language is high level, Enfragmo provides combinatorial problem-solving capability to users without expertise in advanced solver technology. On the other hand, some search problems, e.g., the task of constructing a logistics service provider relying on local service providers, are inherently modular. The framework is extended to represent a modular system. It allows one to combine modules on an abstract model-theoretic level, independently from what languages are used for describing them. In this thesis, an algorithm for finding solutions to such modular systems is proposed. We show that our algorithm closely corresponds to what is done in practice in different areas such as Satisfiability Modulo Theories, Integer Linear Programming, and Answer Set Programming

Enfragmo: A System for Grounding Extended First-Order Logic to SAT

Computationally hard search and optimization problems occur widely in engineering, business, science and logistics, in domains ranging from hardware and software design and verification, to drug design, planning and scheduling. Most of these problems are NP-complete, so no known polynomial-time algorithms exist. Usually, the available solution for a user facing such problems involves mathematical programming for example, integer-linear programming tools, constraint logic programming tools and development of custom-designed implementations of algorithms for solving NP-hard problems. Successful use of these approaches normally requires a deep knowledge of programming, and is often time consuming. Another approach to attack NP search problems is to utilize the knowledge of users to produce precise descriptions of the (search) problem in a declarative specification or modelling language. A solver then takes a specification, together with an instance of the problem, and produces a solution to the problem, if there is any. Model expansion (MX), the logical task of expanding a given (mathematical) structure by new relations, is one of the well-studied directions of this approach. Formally, in MX, the user axiomatizes their problem in a language. This axiomatization describes the relationship between an instance of the problem (a given finite structure, i.e., a universe together with some relations and functions), and its solutions (certain expansions of that structure). This thesis presents the Enfragmo system for specifying and solving combinatorial search problems. Enfragmo takes a problem specification, in which the axioms are expressed in an extension of first-order logic, and a problem instance as its input and produces a propositional conjunctive normal form formula that is sent to a propositional satisfiability (SAT) solver. In this thesis, we describe several techniques that we have developed in order to build our well performing solver, Enfragmo