Related papers: Distribution-Free Normal Modal Logics
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
Language models have become very popular recently and many claims have been made about their abilities, including for commonsense reasoning. Given the increasingly better results of current language models on previous static benchmarks for…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…
We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…
Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality…
This paper develops stable canonical rules for intuitionistic modal logics, which were first introduced for superintuitionistic logics and transitive nor mal modal logics in [1] and [2] respectively. We first prove that every in…
The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Constructive dualities have been recently proposed for some lattice based algebras and a related project has been outlined by Holliday and Bezhanishvili, aiming at obtaining "choice-free spatial dualities for other classes of algebras…
The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…
In this article, we define general normal forms for any logic that has propositional part and whose non-propositional connectives distribute over the finite disjunctions. We do not require the non-propositional connectives to be closed on…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz…
Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies…
Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of…
We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of…
Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead…
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.…
We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof…
We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a…