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The logic of Peirce algebras

Maarten De Rijke

Journal of Logic, Language and Information 4 (3):227-250 (1995)

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Peirce’s Contributions to Possible-Worlds Semantics.Ahti-Veikko Pietarinen - 2006 - Studia Logica 82 (3):345-369.details A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs. The contribution of the GAMMA part of EGs to the study of modalities is examined. Some ramifications of Peirce's remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce's unpublished manuscript on modality from 1901. Download Export citation Bookmark 11 citations
A system of dynamic modal logic.Maarten de Rijke - 1998 - Journal of Philosophical Logic 27 (2):109-142.details In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations (...) Download Export citation Bookmark 10 citations
Zooming in, zooming out.Patrick Blackburn & Maarten De Rijke - 1997 - Journal of Logic, Language and Information 6 (1):5-31.details This is an exploratory paper about combining logics, combining theories and combining structures. Typically when one applies logic to such areas as computer science, artificial intelligence or linguistics, one encounters hybrid ontologies. The aim of this paper is to identify plausible strategies for coping with ontological richness. Download Export citation Bookmark 5 citations
A System of Dynamic Modal Logic.Maarten Rijkdee - 1998 - Journal of Philosophical Logic 27 (2):109-142.details In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations (...) Download Export citation Bookmark 1 citation
Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and Communication.Ahti-Viekko Pietarinen - 2006 - Dordrecht, Netherland: Springer.details Charles Sanders Peirce was one of the United States’ most original and profound thinkers, and a prolific writer. Peirce’s game theory-based approaches to the semantics and pragmatics of signs and language, to the theory of communication, and to the evolutionary emergence of signs, provide a toolkit for contemporary scholars and philosophers. Drawing on unpublished manuscripts, the book offers a rich, fresh picture of the achievements of a remarkable man. Download Export citation Bookmark 12 citations
The Modal Multilogic of Geometry.Philippe Balbiani - 1998 - Journal of Applied Non-Classical Logics 8 (3):259-281.details ABSTRACT A spatial logic is a modal logic of which the models are the mathematical models of space. Successively considering the mathematical models of space that are the incidence geometry and the projective geometry, we will successively establish the language, the semantical basis, the axiomatical presentation, the proof of the decidability and the proof of the completeness of INC, the modal multilogic of incidence geometry, and PRO, the modal multilogic of projective geometry. Download Export citation Bookmark 7 citations

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