Related papers: Intuitionistic modal logics: a minimal setting
Under the Curry--Howard isomorphism, the syntactic structure of programs can be modeled using birelational Kripke structures equipped with intuitionistic and modal relations. Intuitionistic relations capture scoping through persistence,…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of `maximal formula', `segment' and…
We present the logic IBV, which is an intuitionistic version of BV, in the sense that its restriction to the MLL connectives is exactly IMLL, the intuitionistic version of MLL. For this logic we give a deep inference proof system and show…
In previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
In the first part of this paper we analyzed finite non-deterministic matrix semantics for propositional non-normal modal logics as an alternative to the standard Kripke's possible world semantics. This kind of modal systems characterized by…
We present a streamlined and simplified exponential lower bound on the length of proofs in intuitionistic implicational logic, adapted to Gordeev and Haeusler's dag-like natural deduction.
We present three different functional interpretations of intuitionistic linear logic ILL and show how these correspond to well-known functional interpretations of intuitionistic logic IL via embeddings of IL into ILL. The main difference…
I show that propositional intuitionistic logic is complete with respect to an adaptation of Dummett's pragmatist justification procedure. In particular, given a pragmatist justification of an argument, I show how to obtain a natural…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended…
C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater…
Intentions are crucial for our practical reasoning. The rational intention obeys some simple logical principles, such as agglomeration and consistency, among others, motivating the search for a proper logic of intention. However, such a…
In this paper we provide a simplified semantics for the logic KD45(G), i.e. the many-valued G\"odel counterpart of the classical modal logic KD45. More precisely, we characterize KD45(G) as the set of valid formulae of the class of…
We explore an inquisitive modal logic designed to reason about neighborhood models. This logic is based on an inquisitive strict conditional operator, which quantifies over neighborhoods, and which can be applied to both statements and…
We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to descriptive conditional frames, and then introducing the…
This paper is about the computability of the modal definability problem in classes of frames determined by Euclidean modal logics. We characterize those Euclidean modal logics such that the classes of frames they determine give rise to an…
We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates…