On static logics, dynamic logics, and complexity classes

Logics for complexity classes

A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered structures, and another form to define them on unordered non-Aristotelian structures. Using the canonical forms, logics are developed for complete problems in various ...

On a syntactic approximation to logics that capture complexity classes

We formulate a formal syntax of approximate formulas for the logic with counting quantifiers, SOLP, studied by us in [1], where we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P andNL; (ii) weakening the ordering relation to an almost order (in the sense of [7]) we can separate meani...

Computational complexity of propositional dynamic logics

When Do Fixed Point Logics Capture Complexity Classes?

We give examples of classes of rigid structures which are of unbounded rigidity but Least xed point (Partial xed point) logic can express all Boolean PTIME (PSPACE) queries on these classes. This shows that deenability of linear order in FO+LFP although suucient for it to capture Boolean PTIME queries, is not necessary even on the classes of rigid structures. The situation however appears very ...

The complexity of hybrid logics over restricted frame classes

This dissertation examines the computational complexity of decision problems for a collection of hybrid logics over different classes of frames. Hybrid logics are extensions of modal logic that allow, in addition to the usual perspective on states and their successors in relational structures, for naming and accessing states of a structure explicitly. These features are very desirable in many a...