Several proof translations of classical mathematics into intuitionistic mathematics have been proposed in the literature over the past century. These are normally referred to as negative translations or double-negation translations. Among those, the most commonly cited are translations due to Kolmogorov, Gödel, Gentzen, Kuroda and Krivine (in chronological order). In this paper we propose a fra...

Let L be a bounded distributive lattice. We give several characterizations of those Ln → L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and meets. Moreover, we discuss the disjunctive normal form representations of these polynomial functions.

Article history: Received 13 July 2011 Received in revised form 18 November 2011 Accepted 10 February 2012 Available online 14 February 2012

We consider two well-known algebraic proof systems: Polynomial Calculus (PC) and Polynomial Calculus with Resolution (PCR), a system introduced in [2] which combines together PC and Resolution. Moreover we introduce an algebraic proof system PCRk , which combines together Polynomial Calculus (PC) and k-DNF Resolution (RESk). This is a natural generalization to RESk of PCR. In the paper we study...

Some explanations in social science, psychology and biology belong to a higher level than other explanations. And higher explanations possess the virtue of abstracting away from the details of lower explanations, many philosophers argue. As a result, these higher explanations are irreplaceable. And this suggests that there are genuine higher laws or patterns involving social, psychological and ...

The systematic conjunction and disjunction fallacies seen in people’s probability judgments appear to show that people do not reason according to the rules of probability theory. In an experiment examining people’s judgments of the probability of different medical conditions, we find evidence against this view. In this experiment people’s probability judgments closely followed the fundamental ‘...

Let F (p), p ≥ 2 be the family of generalized Thompson’s groups. Here F (2) is the famous Richard Thompson’s group usually denoted by F . We find the growth rate of the monoid of positive words in F (p) and show that it does not exceed p + 1/2. Also we describe new normal forms for elements of F (p) and, using these forms, we find a lower bound for the growth rate of F (p) in its natural genera...

Input Cover Number (denoted by ) is introduced as a metric for diÆculty of propositional resolution derivations. If F = fCig is the input CNF formula, then F(D) is de ned as the minimum number of clauses Ci needed to form a superset of (i.e., cover) clause D. Input Cover Number provides a re nement of the clause-width metric in the sense that it applies to families of formulas whose clause widt...