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We give an exposition in modern language (and using partial orders) of
Jech's method for obtaining models where successor cardinals have
large cardinal properties. In such models, the axiom of choice must
necessarily fail. In particular, we show how, given any regular
cardinal and a large cardina...
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Quantum Kripke frames and other related kinds of Kripke frames are introduced. The inner structures of these Kripke frames are studied in detail, and many of them turn out to form nice geometries. To be precise, geometric frames, which are more general than quantum Kripke frames, correspond to pr...
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I characterize the first-order definable, bi-orthogonally closed subsets of a quasi-quantum Kripke frame satisfying a reasonable assumption. The techniques are generalization of those in Goldblatt's paper published in 1984. Combining these techniques with Goldblatt's idea, I prove that quantum Kr...
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Using the isomorphism from Bezhanishvili et al. 2010 between the category Pries of Priestley spaces and the category PStone of pairwise Stone spaces we construct a Vietoris hyperspace functor on the category PStone related to the Vietoris hyperspace functor on the category Pries from Bezhanishvil...
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In the setting of concurrency theory, Joyal, Winskel and Nielsen introduced a general notion of path bisimulation and showed that path bisimulations can be characterized as spans of open maps between presheaves. A modal logic for presheaves, called path logic, was shown to be expressive for such ...
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We give a general definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence. We describe how this framework specializes to unary modalities and further investigate the operators and semantics to...
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In this paper we explore the relation between an agent’s doxastic attitude and her arguments in support of a given claim. Formally, we build further on Dung's argumentation framework in Dung (1995). We start by introducing a logic to reason about binary arguments which are either in favor or agai...
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In 1935 and 1936 Johansson and Heyting exchanged a series of letters. This exchange inspired Johansson to develop his minimal logic which he ultimately published in an article in 1937. This report summarises Johansson's article and letters, and discusses a number of interesting details of the let...
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These lecture notes cover classical model-theoretic results about modal logic over both models and frames, as developed up to about 1980. They also cover algebraic perspectives on modal logic, and the interplay of model-theoretic and algebraic techniques. Finally, they include some modern themes ...
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In constructive mathematics, equivalences of various properties of cofinite subsets of natural numbers can no longer be proven. In this report, a number of these properties are investigated for subsets of natural numbers as well as binary relations on natural numbers.
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The apparent inconsistency of subjects’ answers in logical reasoning tasks, along with the fact that these answers do not comply with those predicted by classical logic, has been used to argue that human reasoning can not be described adequately by any logical formalism. In particular, Byrne devi...