Related papers: Church's thesis is questioned by new calculation p…
Constructive arithmetic, or the Markov arithmetic MA, is obtained from intuitionistic arithmetic HA by adding the following two principles: the Markov principle M which distinguishes constructivism from intuitionism, and the so-called…
An automaton is called reachable if every state is reachable from the initial state. This notion has been generalized coalgebraically in two ways: first, via a universal property on pointed coalgebras, namely, that a reachable coalgebra has…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We investigate the spectral properties of rooted trees with the intention of improving the currently existing results that deal with this matter. The concept of an assigned rational function is recursively defined for each vertex of a…
We turn `the' Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies, and causes for misunderstanding, concerning the…
We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical,…
Markov's principle is a statement that originated in the Russian school of Constructive Mathematics and stated originally that "if it is impossible that an algorithm does not terminate, then it will terminate". This principle has been…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Two aspects of the physical side of the Church-Turing thesis are discussed. The first issue is a variant of the Eleatic argument against motion, dealing with Zeno squeezed time cycles of computers. The second argument reviews the issue of…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…
We exhibit a sound and complete implicit-complexity formalism for functions feasibly computable by structural recursions over inductively defined data structures. Feasibly computable here means that the structural-recursive definition runs…
This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack…
We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some…
We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…
Kleene's computability theory based on the S1-S9 computation schemes constitutes a model for computing with objects of any finite type and extends Turing's 'machine model' which formalises computing with real numbers. A fundamental…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
Jay and Given-Wilson have recently introduced the Factorisation (or SF-) calculus as a minimal fundamental model of intensional computation. It is a combinatory calculus containing a special combinator, F, which is able to examine the…
The Green's function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been…
This paper outlines new paradigms for real analysis and computability theory in the recently proposed non-Aristotelian finitary logic (NAFL). Constructive real analysis in NAFL (NRA) is accomplished by a translation of diagrammatic concepts…