Related papers: From Many-Valued Consequence to Many-Valued Connec…
This paper studies properties of the logic BV, which is an extension of multiplicative linear logic (MLL) with a self-dual non-commutative operator. BV is presented in the calculus of structures, a proof theoretic formalism that supports…
Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By…
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with…
This paper is focused on the study of modal logics defined from valued Kripke frames, and particularly, on computability and expressibility questions of modal logics of transitive Kripke frames evaluated over certain residuated lattices. It…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of…
The conditionally Markov (CM) sequence contains several classes, including the reciprocal sequence. Reciprocal sequences have been widely used in many areas of engineering, including image processing, acausal systems, intelligent systems,…
The family of relevant logics can be faceted by a hierarchy of increasingly fine-grained variable sharing properties -- requiring that in valid entailments $A\to B$, some atom must appear in both $A$ and $B$ with some additional condition…
The Tarskian classical relevant logic TR arises from Tarski's work on the foundations of the calculus of relations and on first-order logic restricted to finitely many variables, presented by Tarski and Givant their book, A Formalization of…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A particular kind of rational relations is the sequential functions. Sequential functions are the functions that…
The approach taken by Gheorghiu, Gu and Pym in their paper on giving a Base-extension Semantics for Intuitionistic Multiplicative Linear Logic is an interesting adaptation of the work of Sandqvist for IPL to the substructural setting. What…
Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective…
We define and study multiplicative connections in the tangent bundle of a Lie groupoid. Multiplicative connections are linear connections satisfying an appropriate compatibility with the groupoid structure. Our definition is natural in the…
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…
We show that for Multiplicative Exponential Linear Logic (without weakenings) the syntactical equivalence relation on proofs induced by cut-elimination coincides with the semantic equivalence relation on proofs induced by the multiset based…
We present a consequence-based calculus for concept subsumption and classification in the description logic ALCHOIQ, which extends ALC with role hierarchies, inverse roles, number restrictions, and nominals. By using standard…
These results are a contribution to the model theory of matrix consequence. We give a semantic characterization of uniform and couniform consequence relations. These properties have never been treated individually, at least in a semantic…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…