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Annihilators and deductive systems in commutative Hilbert algebras

Ivan Chajda, Radomír Halaš, Young Bae Jun (2002)

Commentationes Mathematicae Universitatis Carolinae

The properties of deductive systems in Hilbert algebras are treated. If a Hilbert algebra H considered as an ordered set is an upper semilattice then prime deductive systems coincide with meet-irreducible elements of the lattice Ded H of all deductive systems on H and every maximal deductive system is prime. Complements and relative complements of Ded H are characterized as the so called annihilators in H .

Annihilators in BCK-algebras

Radomír Halaš (2003)

Czechoslovak Mathematical Journal

We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra 𝒜 . We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice 𝒟 ( A ) of all deductive systems on 𝒜 . Moreover, relative annihilators of C 𝒟 ( A ) with respect to B 𝒟 ( A ) are introduced and serve as relative pseudocomplements of C w.r.t. B in 𝒟 ( A ) .

Approches des grammaires catégorielles

Frédérique Segond (1990)

Mathématiques et Sciences Humaines

Étant donné l'importance que prennent les grammaires catégorielles dans le domaine de la linguistique computationnelle, il nous a semblé intéressant de dresser un panorama sur cette question. Nous espérons fournir, aux chercheurs intéressés, un matériau de base susceptible de les aider à approfondir par eux-mêmes le sujet.

Automatic risk control based on FSA methodology adaptation for safety assessment in intelligent buildings

Jerzy Mikulik, Mirosław Zajdel (2009)

International Journal of Applied Mathematics and Computer Science

The main area which Formal Safety Assessment (FSA) methodology was created for is maritime safety. Its model presents quantitative risk estimation and takes detailed information about accident characteristics into account. Nowadays, it is broadly used in shipping navigation around the world. It has already been shown that FSA can be widely used for the assessment of pilotage safety. On the basis of analysis and conclusion on the FSA approach, this paper attempts to show that the adaptation of this...

Axiomatizing omega and omega-op powers of words

Stephen L. Bloom, Zoltán Ésik (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.

Axiomatizing omega and omega-op powers of words

Stephen L. Bloom, Zoltán Ésik (2010)

RAIRO - Theoretical Informatics and Applications

In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.

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