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On the complexity of some substructural logics

Buszkowski W.

Reports on Mathematical Logic

2008

No. 43

5-24

We use a syntactic interpretation of MALL in BCI with logical and , defined in [5], to prove the undecidability of the consequence relations for BCI with logical and and BCI with logical or , and the NP-completeness of BCI. Similar results are obtained for a variant of the Lambek calculus.

Rough Sets and Learning by Unification

Buszkowski W.

Fundamenta Informaticae

2007

Vol. 75, nr 1-4

107-121

We apply basic notions of the theory of rough sets, due to Pawlak], to explicate certain properties of unification-based learning algorithms for categorial grammars, introduced in and further developed in e.g]. The outcomes of these algorithms can be used to compute both the lower and the upper approximation of the searched language with respect to the given, finite sample. We show that these methods are also appropriate for other kinds of formal grammars, e.g. context-free grammars and context-sensitive grammars.

A representation theorem for co-diagonalizable algebras

Buszkowski W.

Reports on Mathematical Logic

2004

Nr 38

13-22

Tadeusz Prucnal [5] published a proof of the following representation theorem: for every atomic co-diagonalizable algebra D there exists an embedding h form D into the field of all subsets of a topological space X such that, for all a ? D, h (?(a)) is the derivative of the set h (a). He presented this results on a conference in Poland in 1983 and left open the question of it could be generalized to all co-diagonizable algebras. It was my observation that some ideas of measure theory (extending a measure to a complete measure) could be applied to define an embedding of any co-diagonalizable algebra into an atomic co-diagonalizable algebra. Consequently, Prucnal's representation theorem holds true for arbitrary co-diagonalizable algebra, witch has been published in our common paper [3]. Two years alter, I've published a short note [2] examining a more general situation of embeddability of modal structures into atomic modal structures. This paper surveys these results with modified proofs and additional comments.