Related papers: Peirce's Truth-functiona Analysis and the Origin o…
Prior research in computational argumentation has mainly focused on scoring the quality of arguments, with less attention on explicating logical errors. In this work, we introduce four sets of explainable templates for common informal…
Modern foundational models increasingly reflect not just world knowledge, but patterns of human preference embedded in their training data. We hypothesize that recursive alignment-via human feedback and model-generated corpora-induces a…
In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR…
The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we…
Causal inference, a critical tool for informing business decisions, traditionally relies heavily on structured data. However, in many real-world scenarios, such data can be incomplete or unavailable. This paper presents a framework that…
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit…
The "openness" of a complex polynomial mapping is discussed and applied to the Fundamental Theorem of Algebra. In this category fall proofs of S. Wolfenstein, R.L. Thompson, J. Milnor, and S. Reich-S. Smale. These proofs take into account…
In this work we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vectors formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in…
This paper is a follow-up to "Models of PT${}^-$ with internal induction for total formulae." We give a strenghtening of the main result on the semantical non-conservativity of the theory of PT${}^-$ with internal induction for total…
A paradox associated with the astrophysical Poynting-Robertson effect is presented. The paradox arises when relativity theory and Mie's solution of Maxwell's equations are confronted with the statements on the Poynting-Robertson effect.…
This paper presents a formal theory of Krivine's classical realisability interpretation for first-order Peano arithmetic ($\mathsf{PA}$). To formulate the theory as an extension of $\mathsf{PA}$, we first modify Krivine's original…
Ernst Zermelo's axiomatization of set theory (1908) did not exclude `a set that is a member of itself'. We call a set that is a member of itself `an individual'. In this article we prove the elimination of Russell's paradox is equivalent to…
Upon reading Einstein's views on quantum incompleteness in publications or in his correspondence after 1935 (the EPR paradox), one gets a very intense feeling of deja-vu. Einstein presents a quantum hole argument, which somewhat reminds of…
Recent probing studies reveal that large language models exhibit linear subspaces that separate true from false statements, yet the mechanism behind their emergence is unclear. We introduce a transparent, one-layer transformer toy model…
In this paper I outline my propensiton version of quantum theory (PQT). PQT is a fully micro-realistic version of quantum theory that provides us with a very natural possible solution to the fundamental wave/particle problem, and is free of…
This paper (1)shows that the best supported current psychological theory (Cheng, 1997) of how human subjects judge the causal power or influence of variations in presence or absence of one feature on another, given data on their…
In 1935, Einstein, Podolsky, and Rosen (EPR) claimed the incompleteness of quantum mechanics based on the notions of realism (``{\it If, without in any way disrupting a system, we can predict with certainty - i.e., with a probability of one…
There is a growing concern that the recent progress made in AI, especially regarding the predictive competence of deep learning models, will be undermined by a failure to properly explain their operation and outputs. In response to this…
Pre-trained Language Models (PLMs) encode various facts about the world at their pre-training phase as they are trained to predict the next or missing word in a sentence. There has a been an interest in quantifying and improving the amount…