We characterize computationally the functions provable in second order logic with set existence restricted to natural classes of rst order formulas. A classi cation of rst-order set-existence by implicational rank yields a natural hierarchy of complexity classes within the class of Kalmar-elementary functions: The functions over f0; 1g constructively provable using set existence for formulas of...

Closure system on a finite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of finite lattices, and the tools of economic description of a finite lattice have long existed in lattice theory. We present this approach by describing the so-called D-basis and introducing the concept of ordered direct basis of an impli...

In this note we show how any formula δ with a proof of super-polynomial size in M→ has a poly-sized proof in K→ . This fact entails that any propositional classical tautology has short proofs, i.e., NP=CoNP. 1 Every classical tautology has short proofs This article reports the results on the investigation on the existence of short proofs for every Classical Propositional Logic tautology. Firstl...

A minimal formula of a given logic L is a formula which is provable in L and is not a non-trivial substitution instance of other provable formulas in L. In [5], Y. Komori asked whether normal proofs of minimal formulas are unique in the implicational fragments of natural deduction systems for the intuitionistic logic and the logic BCK. It was already shown that the answer is positive for BCK, w...

The discovery of general patterns and their subsequent explanation is a familiar method in linguistics and other cross-cultural research. This paper addresses the computerized enumeration of significant cultural and linguistic patterns, specifically implicational universals. We dispute published suggestions that the mechanical generation of universals is inadvisable, by arguing that such claims...

In this article, I discuss the so-called implicational and-construction and show how it can be derived under Minimalist assumptions. e major challenge is to nd a way to account for the subordinate and the coordinate properties of this construction at the same time. e crucial idea behind the analysis is that the asymmetric syntax of coordination enables the transformation of a subordinate struc...

This is the continuation of the paper [4]. We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-p...

The epigenetic alterations like histone modifications , DNA methylation and others remarkable categories  including nucleosome remodeling and RNA mediated targeting have been strongly investigated  recently .In this way , beside the notable importance of DNA methylation ,the histone modifications are the most important issues in the  tumorogenesis and cancer progression. Moreover...