Association rules are essential data mining tool and as such has been well researched. Many new types of association rules based on both categorial or quantitative data have been founded ([8], [7], [2], [4]). Our work is directed to the theoretical features of association rules; especially, we study a specific class of association rules called δ-cosymmetric rules. We present here some interesti...

Epistemic indefinites (henceforth EIs) are existentials that when used in a positive context convey information about the speaker’s epistemic state (e.g. Jayez and Tovena, 2006, Alonso-Ovalle and Menéndez-Benito, 2010): they signal that the speaker is unable to identify the individual that satisfies the existential claim. In some languages EIs can also be used in negative contexts to convey nar...

The aim of this paper is to investigate a Curry-Howard interpretation of the intersection and union type inference system for Combinatory Logic. Types are interpreted as formulas of a Hilbert-style logic L, which turns out to be an extension of the intuitionistic logic with respect to provable disjunctive formulas (because of new equivalence relations on formulas), while the implicational-conju...

Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing approaches to Cut-admissibility. We decorate proofs with proofterms and introduce various term-reduction systems representing proof transformations. In contrast to previous papers which ga...

In this paper, we describe a simple randomized algorithm that runs in polynomial time and solves connected row convex (CRC) constraints in distributed settings. CRC constraints generalize many known tractable classes of constraints like 2SAT and implicational constraints. They can model problems in many domains including temporal reasoning and geometric reasoning, and generally speaking, play t...

In this paper we investigate, for intuitionistic implicational logic, the relationship between normalization in natural deduction and cut-elimination in a standard sequent calculus. First we identify a subset of proofs in the sequent calculus that correspond to proofs in natural deduction. Then we define a reduction relation on those proofs that exactly corresponds to normalization in natural d...

The assertional logic S(BCIA) of the quasivariety of BCI-algebras (in Iseki's sense) is axiomatized, relative to pure implicational logic BCI, by the rule x, y, x → y (G) (see [1]). Alternatively, the role of (G) can be played by x x → (y → y) (1) (see [2]). The formula (x → x) → (y → y) (2) is a theorem of S(BCIA). In [2, Proposition 22] we claimed erroneously that, relative to BCI, the axiom ...

In a previous paper, we have introduced an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the assertional part and by a domain expert. This approach, called knowledge base completion, was based on an extension of attribute exploration to the case of partial contexts. The present paper recalls this ap...

This paper presents the number of results concerning problems of asymptotic densities in the variety of propositional logics. We investigate, for propositional formulas, the proportion of tautologies of the given length n against the number of all formulas of length n. We are specially interested in asymptotic behavior of this fraction. We show what the relation between a number of premises of ...

The purpose of this note is to give a demonstration of the completeness theorem of type assignment system for λ-terms of [Hindley 83] and [Coquand 05] with two directions of slight extensions. Firstly, using the idea of [Okada 96], [Okada-Terui 99] and [Hermant-Okada 07], we extend their completeness theorem to a stronger form which implies a normal form theorem. Secondly, we extend the simple ...