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Grounding FO and FO(ID) with bounds
 J. Artif. Intell. Res. (JAIR
"... Grounding is the task of reducing a firstorder theory and finite domain to an equivalent propositional theory. It is used as preprocessing phase in many logicbased reasoning systems. Such systems provide a rich firstorder input language to a user and can rely on efficient propositional solvers to ..."
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Grounding is the task of reducing a firstorder theory and finite domain to an equivalent propositional theory. It is used as preprocessing phase in many logicbased reasoning systems. Such systems provide a rich firstorder input language to a user and can rely on efficient propositional solvers to perform the actual reasoning. Besides a firstorder theory and finite domain, the input for grounders contains in many applications also additional data. By exploiting this data, the size of the grounder’s output can often be reduced significantly. A common practice to improve the efficiency of a grounder in this context is by manually adding semantically redundant information to the input theory, indicating where and when the grounder should exploit the data. In this paper we present a method to compute and add such redundant information automatically. Our method therefore simplifies the task of writing input theories that can be grounded efficiently by current systems. We first present our method for classical firstorder logic (FO) theories. Then we extend it to FO(ID), the extension of FO with inductive definitions, which allows for more concise and comprehensive input theories. We discuss implementation issues and experimentally validate the practical applicability of our method. 1.
Model Expansion as a Framework for Modelling and Solving Search Problems
"... We propose a framework for modelling and solving search problems using logic, and describe a project whose goal is to produce practically effective, general purpose tools for representing and solving search problems based on this framework. The mathematical foundation lies in the areas of finite mod ..."
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We propose a framework for modelling and solving search problems using logic, and describe a project whose goal is to produce practically effective, general purpose tools for representing and solving search problems based on this framework. The mathematical foundation lies in the areas of finite model theory and descriptive complexity, which provide us with many classical results, as well as powerful techniques, not available to many other approaches with similar goals. We describe the mathematical foundations; explain an extension to classical logic with inductive definitions that we consider central; give a summary of complexity and expressiveness properties; describe an approach to implementing solvers based on grounding; present grounding algorithms based on an extension of the relational algebra; describe an implementation of our framework which includes use of inductive definitions, sorts and order; and give experimental results comparing the performance of our implementation with ASP solvers and another solver based on the same framework. 1.
Reformulating the Situation Calculus and the Event Calculus in the General Theory of Stable Models and in Answer Set Programming
"... Circumscription and logic programs under the stable model semantics are two wellknown nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis ..."
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Circumscription and logic programs under the stable model semantics are two wellknown nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis of a family of action languages, such as language A and several of its descendants. Based on the discovery that circumscription and the stable model semantics coincide on a class of canonical formulas, we reformulate the situation calculus and the event calculus in the general theory of stable models. We also present a translation that turns the reformulations further into answer set programs, so that efficient answer set solvers can be applied to compute the situation calculus and the event calculus. 1.
Connecting firstorder ASP and the logic FO(ID) through reducts
 In: Correct Reasoning: Essays on LogicBased AI in Honor of Vladimir Lifschitz
, 2012
"... on his 65th birthday! Abstract. Recently, an answerset programming (ASP) formalism of logic programing with the answerset semantics has been extended to the full firstorder setting. Earlier an extension of firstorder logic with inductive definitions, the logic FO(ID), was proposed as a knowledge ..."
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on his 65th birthday! Abstract. Recently, an answerset programming (ASP) formalism of logic programing with the answerset semantics has been extended to the full firstorder setting. Earlier an extension of firstorder logic with inductive definitions, the logic FO(ID), was proposed as a knowledge representation formalism and developed as an alternative ASP language. We present characterizations of these formalisms in terms of concepts of infinitary propositional logic. We use them to find a direct connection between the firstorder ASP and the logic FO(ID) under some restrictions on the form of theories (programs) considered. 1
Uniform evaluation of nonmonotonic DLprograms
 In FoIKS’12, volume 7153 of LNCS
, 2012
"... Abstract. Nonmonotonic description logic programs are a major formalism for a loose coupling of rules and ontologies, formalized in logic programming and description logics, respectively. While this approach is attractive for combining systems, the impedance mismatch between different reasoning engi ..."
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Abstract. Nonmonotonic description logic programs are a major formalism for a loose coupling of rules and ontologies, formalized in logic programming and description logics, respectively. While this approach is attractive for combining systems, the impedance mismatch between different reasoning engines and the APIstyle interfacing are an obstacle to efficient evaluation of dlprograms in general. Uniform evaluation circumvents this by transforming programs into a single formalism, which can be evaluated on a single reasoning engine. In this paper, we consider recent and ongoing work on this approach which uses relational firstorder logic (and thus relational database engines) and datalog with negation as target formalisms. Experimental data show that significant performance gains are possible and suggest the potential of this approach. 1
Debugging for model expansion
 in ICLP, volume 5649 of LNCS
, 2009
"... Abstract. Due to the development of efficient solvers, declarative problem solving frameworks based on model generation are becoming more and more applicable in practice. However, there are almost no tools to support debugging in these frameworks. For several reasons, current solvers are not suitab ..."
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Abstract. Due to the development of efficient solvers, declarative problem solving frameworks based on model generation are becoming more and more applicable in practice. However, there are almost no tools to support debugging in these frameworks. For several reasons, current solvers are not suitable for debugging by tracing. In this paper, we propose a new solver algorithm for one of these frameworks, namely Model Expansion, that allows for debugging by tracing. We explain how to explore the trace of this solver in order to quickly locate a bug and we compare our debugging method with existing ones for Answer Set Programming and the Alloy system. 1
SAT modulo graphs: Acyclicity
, 2014
"... Abstract. Acyclicity is a recurring property of solutions to many important combinatorial problems. In this work we study embeddings of specialized acyclicity constraints in the satisfiability problem of the classical propositional logic (SAT). We propose an embedding of directed graphs in SAT, wit ..."
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Abstract. Acyclicity is a recurring property of solutions to many important combinatorial problems. In this work we study embeddings of specialized acyclicity constraints in the satisfiability problem of the classical propositional logic (SAT). We propose an embedding of directed graphs in SAT, with arcs labelled with propositional variables, and an extended SAT problem in which all clauses have to be satisfied and the subgraph consisting of arcs labelled true is acyclic. We devise a constraint propagator for the acyclicity constraint and show how it can be incorporated in offtheshelf SAT solvers. We show that all existing encodings of acyclicity constraints in SAT are either prohibitively large or do not sanction all inferences made by the constraint propagator. Our experiments demonstrate the advantages of our solver over other approaches for handling acyclicity. 1
Lazy model expansion by incremental grounding
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... Model expansion is a widely accepted way to solve a range of problems. It is achieved by encoding the problem in a declarative (logic) language such that structures which satisfy the specification are solutions to the problem. Model expansion is researched in domains like Knowledge Representation an ..."
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Model expansion is a widely accepted way to solve a range of problems. It is achieved by encoding the problem in a declarative (logic) language such that structures which satisfy the specification are solutions to the problem. Model expansion is researched in domains like Knowledge Representation and Answer Set Programming. The groundandsolve methodology tackles model expansion by converting the predicate descriptions of the problem together with the problem instance data to propositional clauses and afterwards applying a model generator for propositional logic. Groundandsolve is currently a stateoftheart approach to model expansion, but a weakness of the approach is that the grounding step is only applicable when the problem instance is finite, and even then the grounding can be exponentially larger than the original description. In this paper we describe a lazy approach to grounding of problems specified in firstorder logic that can cope with large and infinite problem domains. It interleaves grounding and propositional model expansion, and by keeping track whether models found for a subset of the full grounding solve the problem, it can forgo determining all propositions in the grounding. The approach is hence both more widely applicable and more efficient for problems where the grounding is large.
Complexity of expanding a finite structure and related tasks
 The 8th Int. Workshop on Logic and Comput. Complexity (LCC
, 2006
"... The authors of [MT05] proposed a declarative constraint programming framework based on classical logic extended with nonmonotone inductive definitions. In the framework, a problem instance is a finite structure, and a problem specification is a formula defining the relationship between an instance ..."
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The authors of [MT05] proposed a declarative constraint programming framework based on classical logic extended with nonmonotone inductive definitions. In the framework, a problem instance is a finite structure, and a problem specification is a formula defining the relationship between an instance and its solutions. Thus, problem solving amounts to expanding a finite structure with new relations, to satisfy the formula. We present here the complexities of model expansion for a number of logics, alongside those of satisfiability and model checking. As the task is equivalent to witnessing the existential quantifiers in ∃SO model checking, the paper is in large part of a survey of this area, together with some new results. In particular, we describe the combined and data complexity of FO(ID), firstorder logic extended with inductive definitions [DT04] and the guarded and kguarded logics of [AvBN98] and [GLS01]. 1
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 i ..."
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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’s 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 socalled GenerateDefineTest programs.