On the Complexity of Conditional Logics

Nir Friedman; Joseph Y. Halpern

On the Complexity of Conditional Logics

Nir Friedman
, Joseph Y. Halpern

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

55 Scopus citations

Abstract

Conditional logics, introduced by Lewis and Stalnaker, have been utilized in artificial intelligence to capture a broad range of phenomena. In this paper we examine the complexity of several variants discussed in the literature. We show that, in general, deciding satisfiability is PSPACE-complete for formulas with arbitrary conditional nesting and NP-complete for formulas with bounded nesting of conditionals. However, we provide several exceptions to this rule. Of particular note are results showing that (a) when assuming uniformity (i.e., that all worlds agree on what worlds are possible), the decision problem becomes EXPTIME-complete even for formulas with bounded nesting, and (b) when assuming absoluteness (i.e., that all worlds agree on all conditional statements), the decision problem is NP-complete for formulas with arbitrary nesting.

Original language	English
Title of host publication	Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994
Editors	Jon Doyle, Erik Sandewall, Pietro Torasso
Publisher	Association for the Advancement of Artificial Intelligence
Pages	202-213
Number of pages	12
ISBN (Electronic)	155860328X, 9781558603288
State	Published - 1994
Externally published	Yes
Event	4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994 - Bonn, Germany Duration: 24 May 1994 → 27 May 1994

Publication series

Name	Proceedings of the International Conference on Knowledge Representation and Reasoning
ISSN (Print)	2334-1025
ISSN (Electronic)	2334-1033

Conference

Conference	4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994
Country/Territory	Germany
City	Bonn
Period	24/05/94 → 27/05/94

Bibliographical note

Publisher Copyright:
Copyright © 1994 by Morgan Kaufmann Publishers, Inc. All rights reserved.

Cite this

Friedman, N., & Halpern, J. Y. (1994). On the Complexity of Conditional Logics. In J. Doyle, E. Sandewall, & P. Torasso (Eds.), Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994 (pp. 202-213). (Proceedings of the International Conference on Knowledge Representation and Reasoning). Association for the Advancement of Artificial Intelligence.

Friedman, Nir ; Halpern, Joseph Y. / On the Complexity of Conditional Logics. Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994. editor / Jon Doyle ; Erik Sandewall ; Pietro Torasso. Association for the Advancement of Artificial Intelligence, 1994. pp. 202-213 (Proceedings of the International Conference on Knowledge Representation and Reasoning).

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abstract = "Conditional logics, introduced by Lewis and Stalnaker, have been utilized in artificial intelligence to capture a broad range of phenomena. In this paper we examine the complexity of several variants discussed in the literature. We show that, in general, deciding satisfiability is PSPACE-complete for formulas with arbitrary conditional nesting and NP-complete for formulas with bounded nesting of conditionals. However, we provide several exceptions to this rule. Of particular note are results showing that (a) when assuming uniformity (i.e., that all worlds agree on what worlds are possible), the decision problem becomes EXPTIME-complete even for formulas with bounded nesting, and (b) when assuming absoluteness (i.e., that all worlds agree on all conditional statements), the decision problem is NP-complete for formulas with arbitrary nesting.",

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Friedman, N & Halpern, JY 1994, On the Complexity of Conditional Logics. in J Doyle, E Sandewall & P Torasso (eds), Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994. Proceedings of the International Conference on Knowledge Representation and Reasoning, Association for the Advancement of Artificial Intelligence, pp. 202-213, 4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994, Bonn, Germany, 24/05/94.

On the Complexity of Conditional Logics. / Friedman, Nir; Halpern, Joseph Y.
Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994. ed. / Jon Doyle; Erik Sandewall; Pietro Torasso. Association for the Advancement of Artificial Intelligence, 1994. p. 202-213 (Proceedings of the International Conference on Knowledge Representation and Reasoning).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Conditional logics, introduced by Lewis and Stalnaker, have been utilized in artificial intelligence to capture a broad range of phenomena. In this paper we examine the complexity of several variants discussed in the literature. We show that, in general, deciding satisfiability is PSPACE-complete for formulas with arbitrary conditional nesting and NP-complete for formulas with bounded nesting of conditionals. However, we provide several exceptions to this rule. Of particular note are results showing that (a) when assuming uniformity (i.e., that all worlds agree on what worlds are possible), the decision problem becomes EXPTIME-complete even for formulas with bounded nesting, and (b) when assuming absoluteness (i.e., that all worlds agree on all conditional statements), the decision problem is NP-complete for formulas with arbitrary nesting.

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Friedman N, Halpern JY. On the Complexity of Conditional Logics. In Doyle J, Sandewall E, Torasso P, editors, Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning, KR 1994. Association for the Advancement of Artificial Intelligence. 1994. p. 202-213. (Proceedings of the International Conference on Knowledge Representation and Reasoning).

On the Complexity of Conditional Logics

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