A Constraint Logic Approach to Automated Modal Deduction

A general framework for the construction of deductive systems that use modal logic is developed. Sentences in modal logic are translated into a constraint logic in which the constraints represent the accessibility relation in the possible world semantics for these logics. The translation procedure and the constraint logic depend upon the specific modal logic being translated. The framework provides a mechanism for converting a wide variety of first order inference rules into inference rules for a constraint logic. The proofs of soundness and completeness of the constrained inference rules are produced by systematically transforming the proofs for the original inference rules. Special mechanisms are developed for reasoning about the constraints. The integration of these special purpose reasoners and the general deductive system is accomplished by drawing upon general results in the area of hybrid reasoning. It is argued that a number of existing modal deduction methods can be viewed as instances of this general framework. The advantages of the general approach are simple proofs of correctness for various instances of the framework and ease in incorporating additional features not currently available in automated modal deductive systems. The greater expressivity of logics with these additional features is needed in many A.I. applications of modal logic, such as reasoning about knowledge and action.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Scherl, Richard Brian

Contributors dc:contributor

• Frisch, Alan,

• Artificial Intelligence
• Computer Science

Identifier

(UMI)AAI9305681

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72073