Proof systems for Moss’ coalgebraic logic

0455671 - ÚI 2016 NL eng J - Článek v odborném periodiku
Bílková, Marta - Palmigiano, A. - Venema, Y.
Proof systems for Moss’ coalgebraic logic.
Theoretical Computer Science. Roč. 549 (2014), s. 36-60. ISSN 0304-3975. E-ISSN 1879-2294
Impakt faktor: 0.657, rok: 2014

We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced by L. Moss. The logic captures the behaviour of coalgebras for a large class of set functors. The syntax of the logic, defined uniformly with respect to a finitary coalgebraic type functor T, uses a single modal operator del(T) of arity given by the functor T itself, and its semantics is defined in terms of a relation lifting functor (T) over bar. An axiomatization of the logic, consisting of modal distributive laws, has been given together with an algebraic completeness proof in work of C. Kupke, A. Kurz and Y. Venema. In this paper, following our previous work on structural proof theory of the logic in the special case of the finitary powerset functor, we present cut-free, one- and two-sided sequent calculi for the finitary version of Moss' coalgebraic logic for a general finitary functor T in a uniform way. For the two-sided calculi to be cut-free we use a language extended with the boolean dual of the nabla modality.
Trvalý link: http://hdl.handle.net/11104/0256287