Results 1 
7 of
7
Inductive Situation Calculus
 Artificial Intelligence
, 2004
"... see [2]. Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation calculus using the Logic for NonMonotone Inductive Definitions (NMID). This is an extension of classical logic that allows for unifo ..."
Abstract

Cited by 37 (24 self)
 Add to MetaCart
see [2]. Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation calculus using the Logic for NonMonotone Inductive Definitions (NMID). This is an extension of classical logic that allows for uniform representation of various forms of definitions, including monotone inductive definitions and nonmonotone forms of inductive definitions such as iterated induction and induction over wellfounded posets [1]. Here, we demonstrate an application of NMIDlogic. The aim is twofold. First, we illustrate the role of NMIDlogic and nonmonotone inductive definitions for knowledge representation by presenting a variant of the situation calculus which we call inductive situation calculus. We show that ramification rules can be naturally modeled through a nonmonotone iterated inductive definition. Second, we illustrate the use of our recently developed modularity techniques for NMIDlogic in order to translate a theory of the inductive situation calculus into a classical logic theory of Reiter’s situation calculus [3].
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 10 (5 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
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.
A Deductive System for PC(ID) ⋆
"... Abstract. The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with nonmonotone inductive definitions. This paper studies a deductive inference method for PC(ID), its propositional fragment. We introduce a formal proof system based on the sequent calculus (Gen ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract. The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with nonmonotone inductive definitions. This paper studies a deductive inference method for PC(ID), its propositional fragment. We introduce a formal proof system based on the sequent calculus (Gentzenstyle deductive system) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our deductive system integrates inference rules for propositional calculus and definitions. We prove the soundness and completeness of this deductive system for a slightly restricted fragment of PC(ID). We also give a counterexample to show that cutelimination does not hold in this proof system. 1
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 & ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
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).
Computing Science
"... ii We explore the application of MXG, a declarative programming solver for NP search problems based on Model Expansion (MX) for first order logic with inductive definitions. We present specifications for several common NPcomplete benchmark problems in the language of MXG, and describe some modeli ..."
Abstract
 Add to MetaCart
(Show Context)
ii We explore the application of MXG, a declarative programming solver for NP search problems based on Model Expansion (MX) for first order logic with inductive definitions. We present specifications for several common NPcomplete benchmark problems in the language of MXG, and describe some modeling techniques we found useful in obtaining good solver performance. We present an experimental comparison of the performance of MXG with Answer Set Programming (ASP) solvers on these problems, showing that MXG is competitive and often better. As an extended example, we consider an NPcomplete phylogenetic inference problem. We present several specifications for this problem, employing a variety of techniques for obtaining good performance. Our best solution, which combines instance preprocessing, redundant axioms, and symmetry breaking axioms, performs orders of magnitude faster than previously reported declarative programming solutions using ASP solvers. iii iv To my mom and dad. Acknowledgments I would like to thank Dr. David Mitchell, my senior supervisor, for his guidance and support throughout my Masters studies. I thank Dr. Uwe Glasser and Dr. Arvind Gupta for their comments on the final document. I am grateful to Eugenia Ternovska, Jan Manuch, and Sharon (Xiaohong) Zhong for helpful discussions. My thanks to Jonathan Kavanagh for providing his ASP programs. Last but not least I would like to thank Raheleh Mohebali, my beloved partner, and my parents for their endless support. v