Related papers: Unified Correspondence and Proof Theory for Strict…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
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…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational…
We introduce the two substructural propositional logics KL, KL+, which use disjunction, fusion and a unary, (quasi-)exponential connective. For both we prove strong completeness with respect to the interpretation in Kleene algebras and a…
In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N and the logic of first-degree entailment FDE, also known as Belnap-Dunn four-valued…
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 develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka…
Current large language models reason in isolation. Although it is common to sample multiple reasoning paths in parallel, these trajectories do not interact, and often fail in the same redundant ways. We introduce LACE, a framework that…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should…
The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules…
We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two…
Federated inference enhances LLM performance in edge computing through weighted averaging of distributed model predictions. However, autoregressive LLM inference requires frequent full-model forward passes across workers, severely limiting…
Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of tableaux calculi, a refutation approach to display calculi…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
Extended versions of the Lambek Calculus currently used in computational linguistics rely on unary modalities to allow for the controlled application of structural rules affecting word order and phrase structure. These controlled structural…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
Tse and Zdancewic have formalized the notion of noninterference for Abadi et al.'s DCC in terms of logical relations and given a proof of noninterference by reduction to parametricity of System F. Unfortunately, their proof contains errors…
Probabilistic programming languages (PPLs) are an expressive means of representing and reasoning about probabilistic models. The computational challenge of probabilistic inference remains the primary roadblock for applying PPLs in practice.…