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Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…
This paper presents a sound, complete, and decidable analytic tableau system for the logic of evidence and truth \letf, introduced in Rodrigues, Bueno-Soler \& Carnielli (Synthese, DOI: 10.1007/s11229-020-02571-w, 2020). \letf\ is an…
Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of strict finitistic arithmetic. They are tree-like structures, formed in…
In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) published a thought experiment that is entirely correct, has been demonstrated in real experiments, and is now the most famous in quantum physics. Their pioneering work…
In 1988, in cooperation with a team of experimental physicists, a Condensed Matter theorist, X, published in Physical Review Letters a crucial experimental result dealing with a revolutionary new theory. The conclusions of the paper were…
The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure…
Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955]. It is based on a discrete mechanical framework that can be used to model computation over the real numbers. In this context the…
The IFF approach for the notion of "lattice of theories" uses the idea of a concept lattice from Formal Concept Analysis (Ganter and Wille) and the idea of the truth classification from Information Flow (Barwise and Seligman). The IFF…
The aim of this text is to present, in a technically accessible way, Tarski's definition of truth, the indefinability theorem, and to discuss two aspects of Tarski's work on truth, namely, whether or not the definition captures the notion…
Verifying textual claims against structured tabular data is a critical yet challenging task in Natural Language Processing with broad real-world impact. While recent advances in Large Language Models (LLMs) have enabled significant progress…
We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing…
Proof-theoretic semantics (PTS) is normally understood today as Base-Extension Semantics (B-eS), i.e., as a theory of proof-theoretic consequence over atomic proof systems. Intuitionistic logic (IL) has been proved to be incomplete over a…
Probabilistic logic reasoning is a central component of such cognitive architectures as OpenCog. However, as an integrative architecture, OpenCog facilitates cognitive synergy via hybridization of different inference methods. In this paper,…
Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century, best known for his doctrine of falsifiability. His axiomatic formulation of probability, however, is unknown to current…
Hille in 1959 gave a stronger form for the classical implicit function theorem of Cauchy for equations of the type $y = \psi(x,y)$, $x,y$ real or complex, $\psi$ analytic with a condition which determines a radius of convergence of the…
We show how to extract a monotonic learning algorithm from a classical proof of a geometric statement by interpreting the proof by means of interactive realizability, a realizability sematics for classical logic. The statement is about the…
This paper introduces Reflective Empiricism, an extension of empirical science that incorporates subjective perception and consciousness processes as equally valid sources of knowledge. It views reality as an interplay of subjective…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…
Counterfactual explanations (CEs) are methods for generating an alternative scenario that produces a different desirable outcome. For example, if a student is predicted to fail a course, then counterfactual explanations can provide the…
Explainable question answering systems should produce not only accurate answers but also rationales that justify their reasoning and allow humans to check their work. But what sorts of rationales are useful and how can we train systems to…