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Grounding for model expansion in kguarded formulas with inductive definitions
 In IJCAI
, 2007
"... Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies ..."
Abstract

Cited by 7 (4 self)
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Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies a given formula. Their longterm goal is to produce practical tools to solve combinatorial search problems, especially those in NP. In this framework, a problem is encoded in a logic, an instance of the problem is represented by a finite structure, and a solver generates solutions to the problem. This approach relies on propositionalisation of highlevel specifications, and on the efficiency of modern SAT solvers. Here, we propose an efficient algorithm which combines grounding with partial evaluation. Since the MX framework is based on classical logic, we are able to take advantage of known results for the socalled guarded fragments. In the case of kguarded formulas with inductive definitions under a natural restriction, the algorithm performs much better than naive grounding by relying on connections between kguarded formulas and tree decompositions. 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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Cited by 3 (3 self)
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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.
A Method for Solving NP Search Based on Model Expansion and Grounding
, 2007
"... The logical task of model expansion (MX) has been proposed as a declarative constraint programming framework for solving search and decision problems. We present a method for solving NP search problems based on MX for first order logic extended with inductive definitions and cardinality constraints ..."
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Cited by 2 (0 self)
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The logical task of model expansion (MX) has been proposed as a declarative constraint programming framework for solving search and decision problems. We present a method for solving NP search problems based on MX for first order logic extended with inductive definitions and cardinality constraints. The method involves grounding, and execution of a propositional solver, such as a SAT solver. Our grounding algorithm applies a generalization of the relational algebra to construct a ground formula representing the solutions to an instance. We demonstrate the practical feasibility of our method with an implementation, called MXG. We present axiomatizations of several NPcomplete benchmark problems, and experimental results comparing the performance of MXG with stateoftheart Answer Set programming (ASP) solvers. The performance of MXG is competitive with, and often better than, the ASP solvers on the problems studied.
Model Expansion and the Expressiveness of FO(ID) and Other Logics
"... Model expansion problem is a question of determining, given a formula and a structure for a part of the vocabulary of the formula, whether there is an expansion of this structure that satisfies the formula. Recent development of a problemsolving paradigm based on model expansion by (Mitchell & Tern ..."
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Cited by 1 (1 self)
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Model expansion problem is a question of determining, given a formula and a structure for a part of the vocabulary of the formula, whether there is an expansion of this structure that satisfies the formula. Recent development of a problemsolving paradigm based on model expansion by (Mitchell & Ternovska, 2005; Mitchell, Ternovska, Hach, & Mohebali, 2006) posed the question of complexity of this problem for logics used in the paradigm. We discuss the complexity of the model expansion problem for a number of logics, alongside that of satisfiability and model checking. As the task is equivalent to witnessing leading existential secondorder quantifiers in a model checking setting, the paper is in large part a survey of this area together with some new results. In particular, we describe the combined and data complexity of model expansion for FO(ID) (Denecker & Ternovska, 2008), as well as guarded and kguarded logics of (Andréka, van Benthem, & Németi, 1998) and (Gottlob, Leone, & Scarcello, 2001).