Atlas home || Conferences | Abstracts | about Atlas

ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL'07)
August 5-9, 2007
St Anne's College, University of Oxford
Oxford, England

Organizers
Mai Gehrke and Hilary Priestley

On the existence of a continuum of logics in NEXT(KTB).
by
Zofia Kostrzycka
University of Technology, Opole, Poland

Zofia Kostrzycka

On the existence of a continuum of logics in NEXT(\mathbf{KTB})

On the existence of a continuum of logics in NEXT(KTB)

University of Technology
Luboszycka 3, 45-036 Opole, Poland
E-mail z.kostrzycka@po.opole.pl

In this paper we investigate normal modal logics over T₂=KTB ⊕^[¯]² p→ ^[¯]³ p logic. Although the T₂ logic is characterized by the class of reflexive symmetric and two-step transitive frames, there is very few results concerning it.

Yutaka Miyazaki in [2] considered logics determined by the so-called wheel frames. On the base of these frames and by using the splitting technique effectively, he constructed a continuum of normal modal logics over T₂ logic.

In this paper we characterize the wheel frames by formulas written in one variable. On this purpose we take advantage of the infinite sequence of non-equivalent formulas in one variable from [2].

Theorem 1 There is a continuum of normal modal logics over T₂ logic defined by formulas in one variable.

We also characterize the connection between the notion of diameter of a frame with a tail, and locally tabular members in NEXT(T₂).

Theorem 2 Let L ∈ NEXT(T₂) logic and L is characterized by frames with a tail. Then:
L is locally tabular iff L has a finite diameter.

References:

[1] Kostrzycka Z., On formulas in one variable in NEXT(KTB), Bulletin of the Section of Logic, Vol.35:2/3, (2006), 119-131.

[2] Miyazaki Y. Normal modal logics containing KTB with some finiteness conditions, Advances in Modal Logic, Vol.5, (2005), 171-190.

PDF

Date received: April 25, 2007