Related papers: A simplified definition of logically distributive …

Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…

We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…

We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed…

We define a semantics for first-order logic with generalized quantifiers based on double teams. We also define and investigate a notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a…

We firstly show that the standard interpretation of natural quantification in mathematical logic does not provide a satisfying account of its original richness. In particular, it ignores the difference between generic and distributive…

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…

Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…

While argument mining has achieved significant success in classifying argumentative relations between statements (support, attack, and neutral), we have a limited computational understanding of logical mechanisms that constitute those…

We derive multiple program logics, including correctness, incorrectness, and relational Hoare logic, from the axioms of imperative categories: uniformly traced distributive copy-discard categories. We introduce an internal language for…

NLP tasks differ in the semantic information they require, and at this time no single se- mantic representation fulfills all requirements. Logic-based representations characterize sentence structure, but do not capture the graded aspect of…

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…

We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

The paper relates two variants of semantic models for natural language, logical functional models and compositional distributional vector space models, by transferring the logic and reasoning from the logical to the distributional models.…

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty,…

We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally…

We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…

The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…

A new definition for the notion of a (general) $\infty$-category is given.

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…