Related papers: Negational Fragment of Intuitionistic Control Logi…
Kurt G\"odel proved that it is not possible to characterize Intuitionistic Propositional Logic (IPL) by means of finite and deterministic truth-tables. After extending the same result with respect to non-deterministic matrices, we provide a…
Negation in natural language does not follow Boolean logic and is therefore inherently difficult to model. In particular, it takes into account the broader understanding of what is being negated. In previous work, we proposed a framework…
The intuitionistic modal logics considered between Constructive K (CK) and Intuitionistic K (IK) differ in their treatment of the possibility (diamond) connective. It was recently rediscovered that some logics between CK and IK also…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…
We give natural examples of factors of the Muchnik lattice which capture intuitionistic propositional logic (IPC), arising from the concepts of lowness, 1-genericity, hyperimmune-freeness and computable traceability. This provides a purely…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
We derive an intuitionistic version of G\"odel-L\"ob modal logic ($\sf{GL}$) in the style of Simpson, via proof theoretic techniques. We recover a labelled system, $\sf{\ell IGL}$, by restricting a non-wellfounded labelled system for…
Intuitionistic modal logics (IMLs) extend intuitionistic propositional logic with modalities such as the box and diamond connectives. Advances in the study of IMLs have inspired several applications in programming languages via the…
In this article we characterize the equivalent algebraic semantics for the one-variable monadic fragment of the first-order logic ${\cal G} \forall_{\sim}$ defined by F. Esteva, L. Godo, P. H\'ajek and M. Navara in Residuated fuzzy logics…
We introduce a monotone modal analogue of the intuitionistic (normal) modal logic IK using a translation into a suitable (intuitionistic) first-order logic. We axiomatise the logic and give a semantics by means of intuitionistic…
We aim to solve the problem of temporal-constraint learning from demonstrations to reproduce demonstration-like logic-constrained behaviors. Learning logic constraints is challenging due to the combinatorially large space of possible…
We study an intuitionistic version of common knowledge logic (CK), called ICK, which was introduced by J\"ager and Marti. ICK extends intuitionistic propositional logic (IPL) by multiple box modalities interpreted as knowledge operators for…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
We produce a decidable super-intuitionistic normal modal logic of internalised intuitionistic (and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical monotonic non-disjunctive…