Related papers: Gradual Classical Logic for Attributed Objects - E…
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current large-scale reasoning models primarily rely on scaling up training datasets with diverse…
In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the…
Tableaux originate as a decision method for a logical language. They can also be extended to obtain a structure that spells out all the information in a set of sentences in terms of truth value assignments to atomic formulas that appear in…
In sequential logic there is an order in which the atomic propositions in an expression are evaluated. This order allows the same atomic proposition to have different values depending on which atomic propositions have already been…
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…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements)…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
In the concluding remarks of Ontological Promiscuity Hobbs (1985) made what we believe to be a very insightful observation: given that semantics is an attempt at specifying the relation between language and the world, if "one can assume a…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Cognitive theories for reasoning are about understanding how humans come to conclusions from a set of premises. Starting from hypothetical thoughts, we are interested which are the implications behind basic everyday language and how do we…
The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of…
This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external…
We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…