Formal Concept Analysis and its methods for computing minimal implicational bases have been successfully applied to axiomatise minimal ELTBoxes from models, so called bases of GCIs. However, no technique for an adjustment of an existing EL-TBox w.r.t. a new model is available, i.e., on a model change the complete TBox has to be recomputed. This document proposes a method for the computation of ...

In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability of the following problem for these calculi: whether a given finite set of propositional formulas constitutes an adequate axiom system for a fixed proposition...

We describe an alternative construction of an existing canonical representation for definite Horn theories, the Guigues-Duquenne basis (or GD basis), which minimizes a natural notion of implicational size. We extend the canonical representation to general Horn, by providing a reduction from definite to general Horn CNF. We show how this representation relates to two topics in query learning the...

A formalisation of the implicational fragments of two sequent calculi and a sequent-style presentation of natural deduction in Coq is presented. The systems presented are all typed lambda calculi. Based on this formalisation, some general comments on the feasibility of performing meta-theoretic proofs about typed lambda calculi in a proof assistant based on higher-order type theory are made. Co...

This paper investigates cross-linguistic variation in embedded imperatives in terms of syntactic environments in which they can(not) appear, focusing on the availability of embedded imperatives in the clausal complement of verbs and nouns, and relative clauses. I demonstrate that there are four distinct types of languages regarding the possibility of embedded imperatives. I also suggest that th...

Although lattice theory is a rich field dating from Dedekind, Birkhoff and Öre, few studies in FCA use lattice properties to enhance their results. Moreover, out of the many cryptomorphisms associated with lattices, only the ones associating context, lattice and implicational system are effectively studied. CryptoLat is a software implemented in C] which provides an intuitive view on different ...

Herbelin presented (at CSL'94) a simple sequent calculus for minimal implicational logic, extensible to full rst-order intuitionistic logic, with a complete system of cut-reduction rules which is both con uent and strongly normalising. Some of the cut rules may be regarded as rules to construct explicit substitutions. He observed that the addition of a cut permutation rule, for propagation of s...