Related papers: Multi-modalities and non-commutativity/associativi…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, exhibiting a classical…
In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, considering a classical…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be…
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…
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…
Non-iterative normal modal logics are defined by axioms of modal degree 1. In this paper we use calculations with normal forms to determine the set of all possible non-iterative normal modal logics, unimodal propositional extensions of K.…
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…
In this short paper we will discuss the similarities and differences between two semantic approaches to modal logics - non-deterministic semantics and restricted non-deterministic semantics. Generally speaking, both kinds of semantics are…
We study the relation between additivity and deduction theorems in the algebraic semantics of congruential modal logic. Additivity of the modal operator is well-known to imply the local deduction-detachment theorem. Our main theme is that…
The two Girard translations provide two different means of obtaining embeddings of Intuitionistic Logic into Linear Logic, corresponding to different lambda-calculus calling mechanisms. The translations, mapping A -> B respectively to !A -o…
Inquisitive modal logic, InqML, in its epistemic incarnation, extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. We use the natural notion of…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different…
Subexponential logic is a variant of linear logic with a family of exponential connectives--called subexponentials--that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL)…