# Model Expansion as a Framework for Modelling and Solving Search Problems

@inproceedings{Mitchell2007ModelEA, title={Model Expansion as a Framework for Modelling and Solving Search Problems}, author={David G. Mitchell and E. Ternovska}, year={2007} }

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…

## 25 Citations

A METHOD FOR SOLVING NP SEARCH BASED ON MODEL EXPANSION AND GROUNDING

- Computer Science
- 2007

This work presents a method for solving NP search problems based on MX for first order logic extended with inductive definitions and cardinality constraints, and demonstrates the practical feasibility of the method with an implementation, called MXG.

Lazy Model Expansion: Interleaving Grounding with Search

- Computer ScienceJ. Artif. Intell. Res.
- 2015

A theoretical framework and an implementation in the context of the FO(ċ) knowledge representation language for Lazily grounding the theory during search, where instead of grounding all parts of a theory, justifications are derived for some parts of it.

Lazy Model Expansion by Incremental Grounding

- Computer ScienceICLP
- 2012

A lazy approach to model expansion in the context of first-order logic that can cope with large and infinite problem domains and is hence more widely applicable than ground-and-solve.

Building a Knowledge Base System for an Integration of Logic Programming and Classical Logic

- Computer ScienceICLP
- 2008

This paper presents a Knowledge Base project for FO(ID), an extension of classical logic with inductive definitions based on the view of a logic program as a definition and reports on inference systems that combine state-of-the-art techniques of SAT and ASP.

Model Expansion and the Expressiveness of FO ( ID ) and Other Logics

- Computer Science
- 2008

The combined and data complexity of model expansion for FO(ID) (Denecker & Ternovska, 2008), as well as guarded and k-guarded logics of (Andréka, van Benthem, & Németi, 1998) and (Gottlob, Leone, & Scarcello, 2001).

Is computing science?

- Computer ScienceCACM
- 2013

An experimental comparison of the performance of MXG with Answer Set Programming (ASP) solvers on NP search problems based on Model Expansion (MX) is presented, showing that MXG is competitive and often better than previously reported declarative programming solutions using ASP solvers.

MXG : A Model Expansion Grounder and Solver

- Computer Science

MXG, a solver for NP search problems expressed as model expansion (MX), combines a high-level specification with an instance and produces a propositional formula encoding the solutions.

Arithmetic and Modularity in Declarative Languages for Knowledge Representation

- Computer Science
- 2013

This thesis develops an ideal KR language that captures the complexity class NP for arithmetical search problems and guarantees universality and efficiency for solving such problems, and introduces a framework to language-independently combine modules from different KR languages.

Approximate Reasoning in First-Order Logic Theories

- Computer Science, MathematicsKR
- 2008

This paper presents a method to compute from a given theory and finite domain an approximate structure: a structure that approximates all models, and shows confluence of this method and investigates its complexity.

The KB Paradigm and Its Application to Interactive Configuration

- Computer SciencePADL
- 2016

It is shown that multiple functionalities in this domain can be achieved by applying different forms of logical inferences on a formal specification of the configuration domain, and reported on a proof of concept of this approach in a real-life application with a banking company.

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