Related papers: Semantic Analysis of Subexponential Modalities in …
In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish…
We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For $m>0$, let $\mathrm{L}_m$ be the logic defined by axiom $\lozenge^{m+1} p\to \lozenge p\vee p$. We construct filtrations for…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
This paper introduces two sequent calculi for intuitionistic strong L\"ob logic ${\sf iSL}_\Box$: a terminating sequent calculus ${\sf G4iSL}_\Box$ based on the terminating sequent calculus ${\sf G4ip}$ for intuitionistic propositional…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
This paper introduces the logics of super-strict implications that are based on C.I. Lewis' non-normal modal logics S2 and S3. The semantics of these logics is based on Kripke's semantics for non-normal modal logics. This solves a question…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
The exponential modalities of linear logic have been used by various authors to model infinite-dimensional quantum systems. This paper explains how these modalities can also give rise to the complementarity principle of quantum mechanics.…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of concept combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC TR, whose semantics is based on the…
We propose modal Markov logic as an extension of propositional Markov logic to reason under the principle of maximum entropy for modal logics K45, KD45, and S5. Analogous to propositional Markov logic, the knowledge base consists of…
We enrich the Lambek calculus with the cyclic shift operation, which is expected to model the closure operator of formal languages with respect to cyclic shifts. We introduce a Gentzen-style calculus and prove cut elimination. Secondly, we…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
Lambek calculus with a relevant modality $!\mathbf{L^*}$ of arXiv:1601.06303 syntactically resolves parasitic gaps in natural language. It resembles the Lambek calculus with anaphora $\mathbf{LA}$ of (J\"ager, 1998) and the Lambek calculus…
We define when a ternary term $m$ of an algebraic language $\mathcal{L}$ is called a \textit{distributive nearlattice term} (DN-term) of a sentential logic $\mathcal{S}$. Distributive nearlattices are ternary algebras generalising Tarski…
The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings…
We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
The usual semantics of multi-agent epistemic logic is based on Kripke models, defined in terms of binary relations on a set of possible worlds. Recently, there has been a growing interest in using simplicial complexes rather than graphs, as…
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…