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LOGICS FOR PROPOSITIONAL DETERMINACY AND INDEPENDENCE

  • VALENTIN GORANKO (a1) and ANTTI KUUSISTO (a2)
Abstract

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic ${\cal D}$ and Propositional Independence Logic ${\cal I}$ are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics ${{\cal L}_D}$ and ${{\cal L}_{\,I\,}}$ , based on Kripke semantics, and propose them as alternatives for ${\cal D}$ and ${\cal I}$ , respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue that ${{\cal L}_D}$ and ${{\cal L}_{\,I\,}}$ naturally resolve a range of interpretational problems that arise in ${\cal D}$ and ${\cal I}$ . We also obtain sound and complete axiomatizations for ${{\cal L}_D}$ and ${{\cal L}_{\,I\,}}$ .

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*DEPARTMENT OF PHILOSOPHY STOCKHOLM UNIVERSITY STOCKHOLM, SWEDEN and DEPARTMENT OF MATHEMATICS UNIVERSITY OF JOHANNESBURG (VISITING PROFESSORSHIP) JOHANNESBURG, SOUTH AFRICA E-mail: valentin.goranko@philosophy.su.se
FB03: MATHEMATICS/COMPUTER SCIENCE UNIVERSITY OF BREMEN BREMEN, GERMANY E-mail: antti.j.kuusisto@gmail.com
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This document and all that is needed to prepare documents for ASL publications are posted in the ASL Typesetting Office Website, http://www.math.ucla.edu/∼asl/asltex. August 20, 2000.

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  • ISSN: 1755-0203
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