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Modal Boolean Connexive Logics: Semantics and Tableau Approach

Tomasz Jarmużek;  Jacek Malinowski — 2019

Bulletin of the Section of Logic

In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional...

Bayesian Propositional Logic

Tomasz Jarmużek;  Mateusz Klonowski;  Jacek Malinowski — 2017

Bulletin of the Section of Logic

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w , for all w, and give some formal properties of it.

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