Related papers: A Note on the Possibility of Self-Reference in Mat…
Language models excel in various tasks by making complex decisions, yet understanding the rationale behind these decisions remains a challenge. This paper investigates \emph{data-centric interpretability} in language models, focusing on the…
In this paper we share several experiments trying to automatically translate informal mathematics into formal mathematics. In our context informal mathematics refers to human-written mathematical sentences in the LaTeX format; and formal…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
Compositional vector space models of meaning promise new solutions to stubborn language understanding problems. This paper makes two contributions toward this end: (i) it uses automatically-extracted paraphrase examples as a source of…
A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. This theorem says that with arbitrarily large (sampling/frequentist)…
Finite linear temporal logic ($\mathsf{LTL}_f$) is a powerful formal representation for modeling temporal sequences. We address the problem of learning a compact $\mathsf{LTL}_f$ formula from labeled traces of system behavior. We propose a…
In this work, we aim at understanding incompleteness in an abstract way via metamathematical properties of formal theories. We systematically examine the relationships between the following twelve important metamathematical properties of…
In this paper, we argue that formal systems of first order Arithmetic that admit Goedelian undecidable propositions validly are abnormally non-constructive. We argue that, in such systems, the strong representation of primitive recursive…
It is quite well-known from Kurt Godel's (1931) ground-breaking result on the Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are…
The task of reading comprehension (RC), often implemented as context-based question answering (QA), provides a primary means to assess language models' natural language understanding (NLU) capabilities. Yet, when applied to large language…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
Mathematical Theory of Evidence (MTE), a foundation for reasoning under partial ignorance, is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the…
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…
Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…
We show that self-reference can be formalized in Basic logic by means of the new connective @, called "entanglement". In fact, the property of non-idempotence of the connective @ is a metatheorem, which states that a self-entangled sentence…
In the statistical analysis of objects, samples and populations with quantitative variables, in many occasions we are interested in knowing the proportions that exist between the different variables from a same object; if these proportions…