Related papers: Monadic Intuitionistic and Modal Logics Admitting …
The intuitionistic implication and hence the notion of function space in constructive disciplines is both non-geometric and impredicative. In this paper we try to solve both of these problems by first introducing weak exponential objects as…
Game comonads provide categorical semantics for comparison games in Finite Model Theory, thus providing an abstract characterisation of logical equivalence for a wide range of logics, each one captured through a specific choice of comonad.…
G\"odel logic with the projection operator Delta (G_Delta) is an important many-valued as well as intermediate logic. In contrast to classical logic, the validity and the satisfiability problems of G_Delta are not directly dual to each…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three…
The foundations of formal models for epistemic and doxastic logics often rely on certain logical aspects of modal logics such as S4 and S4.2 and their semantics; however, the corresponding mathematical results are often stated in papers or…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
This report first shows the equivalence bewteen several formulations of classical logic in intuitionistic logic (tertium non datur, reductio ad absurdum, Pierce's law). Then it establishes the correctness of the G\"odel-Kolmogorov…
We present a simple theory explaining the construction and the correctness of an incremental and worst-case optimal decision procedure for modal logic with eventualities. The procedure gives an abstract account of important aspects of…
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…
The language of linear temporal logic can be interpreted over the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${{\sf ITL}^{\sf c}}_{\Diamond,\forall}$, recently shown to be decidable by…
Multimodal knowledge graph completion (MKGC) aims to predict missing entities in MKGs. Previous works usually share relation representation across modalities. This results in mutual interference between modalities during training, since for…
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…
We give a new presentation of interactive realizability with a more explicit syntax. Interactive realizability is a realizability semantics that extends the Curry-Howard correspondence to (sub-)classical logic, more precisely to first-order…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
Similar to modal connectives, the exponential ! in intuitionistic linear logic (ILL) is not canonical, in the sense that if $i\not= j$ then $!^i F\not\equiv !^j F$. Intuitively, this means that we can mark the exponential with labels taken…
This paper argues that a combined treatment of probabilities, time and actions is essential for an appropriate logical account of the notion of probability; and, based on this intuition, describes an expressive probabilistic temporal logic…
Game semantics allows us to look at basic logical concepts from another side. This approach to logic has a long history, there are plenty of different types of games: provability games, semantic games, etc. And there is an interesting type…
We obtain modal completeness of the interpretability logics ILP_0 and ILR w.r.t. generalized Veltman semantics. Our proofs are based on the notion of smart (full) labels. We also give shorter proofs of completeness w.r.t. generalized…
Linear logic programming uses provability as the basis for computation. In the operational semantics based on provability, executing the additive-conjunctive goal $G_1 \& G_2$ from a program $P$ simply terminates with a success if both…