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We introduce a basic intuitionistic conditional logic IntCK that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that IntCK stands in a very natural relation to other similar logics, like the basic classical conditional logic CK and the basic intuitionistic modal logic IK . As for the basic intuitionistic conditional logic ICK proposed in Weiss (Journal of Philosophical Logic, 48, 447–469, 2019), IntCK extends its language with a diamond-like conditional modality ◊ → , but its ( ◊ → )-free fragment is also a proper extension of ICK . We briefly discuss the resulting gap between the two candidate systems of basic intuitionistic conditional logic and the possible pros and cons of both candidates. [ABSTRACT FROM AUTHOR]

We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing (Journal of Philosophical Logic, 47(2), 259–279, 2018). [ABSTRACT FROM AUTHOR]

In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory (Belnap et al. in Facing the future: agents and choices in our indeterminist world, Oxford University Press, New York, 2001) and the semantics of the epistemic logic with justification from (Artemov and Nogina in Journal of Logic and Computation 15:1059-1073, 2005). The general idea is to understand proving that A as seeing to it that a proof of A is (publicly) available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate. [ABSTRACT FROM AUTHOR]

We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing (2015). Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods. [ABSTRACT FROM AUTHOR]