论文信息 - On Graph Calculi for Multi-modal Logics

On Graph Calculi for Multi-modal Logics

We introduce a method, based on graphical representation, for formulating sound and complete calculi for multi-modal logics. This approach provides uniform tools for expressing and manipulating modal formulas. We illustrate the method by constructing, in a natural manner, correct graph calculi for some multi-modal logics, which may include the global and difference modalities, and may have some special properties.

[1] Herman Geuvers,et al. Natural deduction via graphs: formal definition and computation rules , 2007, Math. Struct. Comput. Sci..

[2] Laurent Catach. Normal Multimodal Logics , 1988, AAAI.

[3] Paulo A. S. Veloso,et al. A Calculus for Graphs with Complement , 2010, Diagrams.

[4] Mario R. F. Benevides,et al. PDL for structured data: a graph-calculus approach , 2014, Log. J. IGPL.

[5] M. de Rijke,et al. Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[6] Mario R. F. Benevides,et al. On a Graph Approach to Modal Logics , 2014, LSFA.

[7] Luis Fariñas del Cerro,et al. Modal Tableaux with Propagation Rules and Structural Rules , 1997, Fundam. Informaticae.

[8] Alessandra Carbone,et al. A new mapping between combinatorial proofs and sequent calculus proofs read out from logical flow graphs , 2010, Inf. Comput..

[9] Paulo A. S. Veloso,et al. On graph reasoning , 2009, Inf. Comput..

[10] Paulo A. S. Veloso,et al. On Graph Refutation for Relational Inclusions , 2011, LSFA.

[11] Claudio Pizzi,et al. Modalities and Multimodalities - With the assistance and collaboration of Juliana Bueno-Soler , 2008, Logic, Epistemology, and the Unity of Science.

[12] M. Fitting. Proof Methods for Modal and Intuitionistic Logics , 1983 .

[13] Sara Negri,et al. Proof Analysis in Modal Logic , 2005, J. Philos. Log..

[14] Ian Horrocks,et al. Computational modal logic , 2007, Handbook of Modal Logic.