Related papers: Constructibility and the P versus NP problem
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
Some of the most obviously correct physical theories - namely string theory and the multiverse - make no testable predictions, leading many to question whether we should accept something as scientific even if it makes no testable…
The fixed-template constraint satisfaction problem (CSP) can be seen as the problem of deciding whether a given primitive positive first-order sentence is true in a fixed structure (also called model). We study a class of problems that…
We show that the satisfiability problem for the quantifier-free theory of product structures with the equicardinality relation is in NP. As an application, we extend the combinatory array logic fragment to handle cardinality constraints.…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
In this paper I present an argument and a general schema which can be used to construct a problem case for any decision theory, in a way that could be taken to show that one cannot formulate a decision theory that is never outperformed by…
We consider abstract-argumentation-theoretic coalition formability in this work. Taking a model from political alliance among political parties, we will contemplate profitability, and then formability, of a coalition. As is commonly…
This paper describes an axiomatic theory BT for constructive mathematics. BT has a predicative comprehension axiom for a countable number of set types and usual combinatorial operations. BT has intuitionistic logic, is consistent with…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…
The problem of team formation in a social network asks for a set of individuals who not only have the required skills to perform a task but who can also communicate effectively with each other. Existing work assumes that all links in a…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call this property the Gaifman property. Gaifman conjectured…
We present a very simple example of a theorem with constructive and non-constructive proofs: the equation c^2 x^2 - (c^2 + c)x + c = 0 has a solution.
This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that…
The nature of the scientific method is controversial with claims that a single scientific method does not even exist. However the scientific method does exist. It is the building of logical and self consistent models to describe nature. The…