Related papers: Permanence as a Principle of Practice
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
I shall argue that a resolution of the PvNP problem requires building an iff bridge between the domain of provability and that of computability. The former concerns how a human intelligence decides the truth of number-theoretic relations,…
Persistence is the first principle of big memory systems. We comprehensively analyze the vertical and horizontal extensions of existing memory hierarchy. Networks are flattening traditional storage hierarchies. We present the…
Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not…
We argue that, although Wittgenstein's reservations on Goedel's interpretation of his own formal reasoning are, indeed, of historical importance, the uneasiness that academicians and philosophers continue to sense, and express, over…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…
This article critically reappraises arguments in support of Cantor's theory of transfinite numbers. The following results are reported: i) Cantor's proofs of nondenumerability are refuted by analyzing the logical inconsistencies in…
This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett's and Dag Prawitz' philosophical motivations and…
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 well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…
For relational monadic formulas (the L\"owenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, projection and forgetting - operations that currently receive much attention in…
Expansions of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N} ; < \rangle$ have been a fertile and active area of research ever since the publication of the seminal papers of B\"uchi and Elgot & Rabin on the…
The famous result of B.~Schweizer and A.~Sklar [Pacific J Math 10(1960) 313--334 - Theorem 8.2] asserts that, given a probabilistic metric space $(X,\mathcal F,t)$, $\mathcal F=\{F_{p,q}:p,q\in X\}$, we have $F_{p_n,q_n}(x)\to F_{p,q}(x)$…
This paper engages the question "Does the consistency of a set of axioms entail the existence of a model in which they are satisfied?" within the frame of the Frege-Hilbert controversy. The question is related historically to the…
In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…
This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: 'What…
In the setting of the modal logic that characterizes modal refinement over modal transition systems, Boudol and Larsen showed that the formulae for which model checking can be reduced to preorder checking, that is, the characteristic…
The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of…