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Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
Moving from the mathematical theory of (abstract) syntax, we develop a general relational theory of symbolic manipulation parametric with respect to, and accounting for, general notions of syntax. We model syntax relying on categorical…
Determinism is (roughly) the thesis that the past determines the future. But efforts to define it precisely have exposed deep methodological disagreements. Standard possible-worlds formulations of determinism presuppose an "agreement"…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
Most approaches for repairing description logic (DL) ontologies aim at changing the axioms as little as possible while solving inconsistencies, incoherences and other types of undesired behaviours. As in Belief Change, these issues are…
The question of what ontological message (if any) is encoded in the formalism of contemporary physics is, to say the least, controversial. The reasons for this state of affairs are psychological and neurobiological. The processes by which…
Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of…
This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an…
The topological properties of field configurations in gauge theory contain important data about the (generalized) global symmetries of the theory as well as potential inconsistencies in the form of gauge anomalies. In this work we modify…
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or…
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…
This paper introduces a new family of cognitive modal logics designed to formalize conjectural reasoning: modal systems in which cognitive contexts extend known facts with hypothetical assumptions in order to explore their consequences.…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
The misunderstanding of the concept of differentials in the theories on calculus of Cauchy-Lebesgue system was exposed in this paper. The defects of the definition of differentials and the associated mistakes in the differentiation of…
In this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal…
The paper addresses the question of whether it is appropriate to talk about `mechanical minds' at all, and whether ChatGPT models can indeed be thought of as realizations of that. Our paper adds a semantic argument to the current debate.…
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…
Existing work investigates the reasoning capabilities of large language models (LLMs) to uncover their limitations, human-like biases and underlying processes. Such studies include evaluations of base LLMs (pre-trained on unlabeled corpora…
In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a…