On this article we provide a relation between two inherently different semantic structures for intuitionistic modal logic. We start by recalling the Heyting Algebras, then defining the language and the axioms for the iS4h intuitionistic calculus. We then proceed to analyse two structures discussed on [4] and their relation. Finally, we discuss about a structure defined on [3, Chapter 6], establishing properties in order for it to be sound with iS4h, and finally conclude that it is semantically equivalent to the other two structures defined by [4].
We answer the question whether all Heyting algebras can appear as the lattice of subterminal objects of an elementary topos in the negative. Concretely, we show that the free Heyting algebra on two generators, hence also on N generators for every N greater than 2, cannot be such a Heyting algebra. The mathematical resu...
Carnap [5] in 1943 noticed that there exist some non-normal valuations that do not respect the usual truth conditions of classical connectives, yet are sound. This finding reveals an asymmetry between the syntax and semantics of classical logic and might be counted as a challenge to the inferentialist program. While se...
J. Jafari, Davood Hosseini· Australasian Journal of Logi...· 0 citations
Close semantics is introduced, a new possible-world semantics for such weak modal logics, and soundness and strong completeness for a range of systems are established.
We study infinitary intuitionistic logic by employing both syntactic and semantic methods. First, we introduce a natural deduction system for infinitary predicate logic and study some of its basic properties. We then extend neighbourhood semantics to this setting, providing a soundness and completeness theorem for this...
This paper provides a constructive decision procedure, that, given a formula, produces either a proof showing the formula to be valid or a finite countermodel falsifying the formula, thus also proving the finite model property for both logics.
Marianna Girlando, Roman Kuznets, Sonia Marin et al.· 1 citation
