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Definable Classes of Models and Frames in Bi-intuitionistic Logic
Guillermo Badia, Tomasz Kowalski, Grigory Olkhovikov
The question of the expressive power of a given logical language with Kripke relational semantics has at least two dimensions: (1) what the language can say about frames, and (2) w…
On connexivity in modal and conditional contexts
Grigory K. Olkhovikov
We define and axiomatize three new logics based on the connexive logic , the modal logic and the conditional logics and …
Conditional reasoning and the shadows it casts onto the first-order logic: the Nelsonian case
Grigory Olkhovikov
We define a natural notion of standard translation for the formulas of conditional logic which is analogous to the standard translation of modal formulas into the first-order logic…
A basic system of paraconsistent Nelsonian logic of conditionals
Grigory K. Olkhovikov
We define a Kripke semantics for a conditional logic based on the propositional logic , the paraconsistent variant of Nelson's logic of strong negation; we axiomatize…
An intuitionistically complete system of basic intuitionistic conditional logic
Grigory Olkhovikov
We introduce a basic intuitionistic conditional logic that we show to be complete both relative to a special type of Kripke models and relative to a standard trans…
Craig interpolation theorem fails in bi-intuitionistic predicate logic
Grigory K. Olkhovikov, Guillermo Badia
In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urqu…