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On Associative Omega-Products

Rędziejowski R.R.

Fundamenta Informaticae

2004

Vol. 60, nr 1-4

333--350

In recent years, a number of classical results connecting rational languages with finite semigroups have been extended to infinite-word languages using the notion of an w-semigroup : a semigroup augmented with an associative infinite product. This paper takes a closer look at the associative infinite product itself. It suggests some improvements and presents a couple of new facts.

Conjoinability in Pregroups

Kiślak-Malinowska A.

Fundamenta Informaticae

2004

Vol. 61, nr 1

29--36

Pregroups are introduced by Lambek as a framework for syntactic analysis of Natural Language; they are algebraic models of Compact Bilinear Logic. In the present paper we consider the problem of conjoinability in the calculus of pregroups. We show that two types are conjoinable in a pregroup iff they are equal in a free group. This result is analogous to Pentus' characterization of conjoinability in the Lambek calculus.