Related papers: An axiomatic system for STIT imagination logic
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…
Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team semantic constructions have been used to generate expressively enriched logics still conserving nice properties, such as compactness or decidability. In contrast,…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
This paper presents Non-Axiomatic Term Logic (NATL) as a theoretical computational framework of humanlike symbolic reasoning in artificial intelligence. NATL unites a discrete syntactic system inspired from Aristotle's term logic and a…
We show that the intuitionistic propositional logic with a Galois connection (IntGC), introduced by the authors, has the finite model property.
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem…
We study propositional and first-order G\"odel logics over infinitary languages which are motivated semantically by corresponding interpretations into the unit interval [0,1]. We provide infinitary Hilbert-style calculi for the particular…
By limiting the range of the predicate variables in a second-order language one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note we provide an infinitary strongly…
We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to descriptive conditional frames, and then introducing the…
We propose an approach to analogical inference that marries the neuro-symbolic computational power of complex-sampled hyperdimensional computing (HDC) with Conceptual Spaces Theory (CST), a promising theory of semantic meaning. CST…
We study scattered piecewise interpretable Hilbert spaces from a model theoretic point of view. We establish strong connections between the Hilbert space structure theorems of [Chevalier Hrushovski 2021] and the model theoretic notions of…
Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information…
This document is written with the intention to describe in detail a method and means by which a computer program can reason about the world and in so doing, increase its analogue to a living system. As the literature is rife and it is…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…
We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
In this work we present an intuitive construction of the quantum logical axiomatic system provided by George Mackey. The goal of this work is a detailed discussion of the results from the paper 'Physical justification for using the tensor…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
In this paper, we discuss different models for human logic systems and describe a game with nature. G\"odel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry…