Investigating finite models of non-classical logics with relation Algebra and REL VIEW

R. Berghammer; R.A. Schmidt

doi:10.1007/11964810_2

Investigating finite models of non-classical logics with relation Algebra and REL VIEW

R. Berghammer, R.A. Schmidt

Formal Methods

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

Abstract

In computer science, scenarios with interacting agents are often developed using modal logic. We show how to interpret modal logic of knowledge in relation algebra. This allows the use of the RELVIEW tool for the purpose of investigating finite models and for visualizing certain properties. Our approach is illustrated with the well-known ‘muddy children’ puzzle using modal logic of knowledge. We also sketch how to treat other non-classical logics in this way. In particular, we explore our approach for computational tree logic and illustrate it with the ‘mutual exclusion’ example.

Original language	English
Title of host publication	Theory and Applications of Relational Structures as Knowledge Instruments II
Subtitle of host publication	International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers
Editors	Harrie Swart, Ewa Orłowska, Gunther Schmidt, Marc Roubens
Place of Publication	Berlin
Publisher	Springer Berlin
Chapter	2
Pages	31-49
Number of pages	19
ISBN (Print)	9783540692232
DOIs	https://doi.org/10.1007/11964810_2
Publication status	Published - 2006

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	4342
ISSN (Print)	0302-9743

Keywords

modal logic
transitive closure
critical section
accessibility relation
mutual exclusion

Access to Document

10.1007/11964810_2

Cite this

Berghammer, R., & Schmidt, R. A. (2006). Investigating finite models of non-classical logics with relation Algebra and REL VIEW. In H. Swart, E. Orłowska, G. Schmidt, & M. Roubens (Eds.), Theory and Applications of Relational Structures as Knowledge Instruments II: International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers (pp. 31-49). (Lecture Notes in Computer Science; Vol. 4342). Springer Berlin. https://doi.org/10.1007/11964810_2

Berghammer, R. ; Schmidt, R.A. / Investigating finite models of non-classical logics with relation Algebra and REL VIEW. Theory and Applications of Relational Structures as Knowledge Instruments II: International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. editor / Harrie Swart ; Ewa Orłowska ; Gunther Schmidt ; Marc Roubens. Berlin : Springer Berlin, 2006. pp. 31-49 (Lecture Notes in Computer Science).

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abstract = "In computer science, scenarios with interacting agents are often developed using modal logic. We show how to interpret modal logic of knowledge in relation algebra. This allows the use of the RELVIEW tool for the purpose of investigating finite models and for visualizing certain properties. Our approach is illustrated with the well-known {\textquoteleft}muddy children{\textquoteright} puzzle using modal logic of knowledge. We also sketch how to treat other non-classical logics in this way. In particular, we explore our approach for computational tree logic and illustrate it with the {\textquoteleft}mutual exclusion{\textquoteright} example.",

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Berghammer, R & Schmidt, RA 2006, Investigating finite models of non-classical logics with relation Algebra and REL VIEW. in H Swart, E Orłowska, G Schmidt & M Roubens (eds), Theory and Applications of Relational Structures as Knowledge Instruments II: International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. Lecture Notes in Computer Science, vol. 4342, Springer Berlin, Berlin, pp. 31-49. https://doi.org/10.1007/11964810_2

Investigating finite models of non-classical logics with relation Algebra and REL VIEW. / Berghammer, R.; Schmidt, R.A.
Theory and Applications of Relational Structures as Knowledge Instruments II: International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. ed. / Harrie Swart; Ewa Orłowska; Gunther Schmidt; Marc Roubens. Berlin: Springer Berlin, 2006. p. 31-49 (Lecture Notes in Computer Science; Vol. 4342).

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

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Berghammer R, Schmidt RA. Investigating finite models of non-classical logics with relation Algebra and REL VIEW. In Swart H, Orłowska E, Schmidt G, Roubens M, editors, Theory and Applications of Relational Structures as Knowledge Instruments II: International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. Berlin: Springer Berlin. 2006. p. 31-49. (Lecture Notes in Computer Science). doi: 10.1007/11964810_2

Investigating finite models of non-classical logics with relation Algebra and REL VIEW

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