Related papers: Paraconsistent G\"{o}del modal logic
Despite the rapid progress of large language models (LLMs), knowledge graph-based question answering (KGQA) remains essential for producing verifiable and hallucination-resistant answers in many real-world settings where answer…
Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model-value beyond mere comprehensible pictures. To…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
We present a modal logic based approach to the so-called endophysical quantum universe. In particular, we treat the problem of preferred bases and that of state reduction by employing an eclectic collection of methods including Baltag's…
The paper develops a version of modal logic that stays completely within the framework provided by quantum principles, and then proves, within the framework of quantum thinking, and in particular without invoking "hidden variables", a…
Let $K$ be a field of characteristic zero and let $\mathfrak{sl}_2 (K)$ be the 3-dimensional simple Lie algebra over $K$. In this paper we describe a finite basis for the $\mathbb{Z}_2$-graded identities of the adjoint representation of…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
We introduce FIK, a natural intuitionistic modal logic specified by Kripke models satisfying the condition of forward confluence. We give a complete Hilbert-style axiomatization of this logic and propose a bi-nested calculus for it. The…
Propositional G\"odel logic extends intuitionistic logic with the non-constructive principle of linearity $A\rightarrow B\ \lor\ B\rightarrow A$. We introduce a Curry-Howard correspondence for this logic and show that a particularly simple…
This paper is an attempt to solve the following problem: given a logic, how to turn it into a paraconsistent one? In other words, given a logic in which \emph{ex falso quodlibet} holds, how to convert it into a logic not satisfying this…
Quantum logic (QL) is a non-classical logic for analyzing the propositions of quantum physics. Modal logic MB, which is a logic that handles the value of the inner product that appears in quantum mechanics, was constructed with the…
We present a first-order linear-time temporal logic for reasoning about the evolution of directed graphs. Its semantics is based on the counterpart paradigm, thus allowing our logic to represent the creation, duplication, merging, and…
The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences…
A normal modal logic is pretransitive, if the modality corresponding to the transitive closure of an accessibility relation is expressible in it. In the present work we establish the finite model property for pretransitive generalizations…
We prove that on any log Fano pair of dimension $n$ whose stability threshold is less than $\frac{n+1}{n}$, any valuation computing the stability threshold has a finitely generated associated graded ring. Together with earlier works, this…
Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…
We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…
The overarching theme of the following pages is that mathematical logic -- centered around the incompleteness theorems -- is first and foremost an investigation of $\textit{computation}$, not arithmetic. Guided by this intuition we will…
The prevalent interpretation of G\"odel's Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the formulation of…
A recent proof, formulated in the symbolic language of modal logic, shows that a well-defined formulation of the possibility mentioned in the title is answered affirmatively. In the paper being commented upon several proposals were made…