An algebraic generalization of Kripke structures
by
Sergio Marcelino
King's College London
Coauthors: Pedro Resende

In [1] the Kripke semantics of classical propositional normal modal logic is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. This algebraic semantics subsumes the traditional algebraic semantics based on lattices with unary operators, and it suggests natural interpretations of modal logic, of possible interest in the applications, in structures that arise in geometry and analysis, such as foliated manifolds and operator algebras, via topological groupoids and inverse semigroups. In this talk I survey some results and examples of [1].

[1] S. Marcelino, P Resende, An algebraic generalization of Kripke structures to appear in Math. Proc. Cambridge Philos. Soc., http://arxiv.org/abs/0704.1886

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Paper reference: arXiv:0704.1886

Date received: June 9, 2008