Results

**1 - 2**of**2**### Modal Logics with Existential Modality, Finite-iteration Modality, and Intuitionistic Base: Decidability and Completeness

, 2005

"... This thesis investigates some modal logics that have been found to be useful in modelling computational phenomena and, therefore, of interest to theoretical computer science---namely, modal intuitionistic logics, logics with finite-iteration modality, and logics with existential modality. We prove a ..."

Abstract
- Add to MetaCart

(Show Context)
This thesis investigates some modal logics that have been found to be useful in modelling computational phenomena and, therefore, of interest to theoretical computer science---namely, modal intuitionistic logics, logics with finite-iteration modality, and logics with existential modality. We prove a number of new general results concerning these logics. In particular, in chapter 3, we prove a general decidability result for intuitionistic modal logics through embedding them into the two-variable monadic second-order guarded fragment GF mon with certain conditions imposed on relations occurring in GF mon -formulas. In chapter 4, we prove the analogue of Makinson theorem for logics with finite-iteration modality, that is that every consistent logic in this language is either a sublogic of the logic of a Kripke frame containing a single reflexive point or a sublogic of the logic of a Kripke frame containing a single irreflexive point; the by-product of the theorem is the decidability of the problem of consistency for effectively finitely axiomatizable logics with finite-iteration modality. In chapter 5, we prove completeness of Hilbert-style axiomatizations of three logics whose language contains an existential modality ###: the minimal normal logic with ###, K# ; its deterministic extension DK# ; and the logic that is CPDL (converse PDL) with a single nominal and ### (this logic is known from the literature as PDL ). Apart from the presentation of the above-mentioned results, the thesis contains, in chapter 2, an overview of background material on modal logics and guarded fragments; this overview can also be read as a concise survey of the field of guarded fragments.

### Negation and Inductive Norms

, 2003

"... In 1982, N. Immerman proved that (positive) least fixed point logic was closed under negation. He used a construction similar to that of Moschovakis [34]: if a logic admits an "inductive norm" that partitions a relation into blocks labelled by integers, then an appropriate "stage c ..."

Abstract
- Add to MetaCart

In 1982, N. Immerman proved that (positive) least fixed point logic was closed under negation. He used a construction similar to that of Moschovakis [34]: if a logic admits an "inductive norm" that partitions a relation into blocks labelled by integers, then an appropriate "stage comparison relation" might be used to construct a negation of that relation within that logic. In this paper, we generalize this construction to many fragments of positive least fixed point logic, and in particular we will find that if such a fragment is closed under (on a class of finite structures), and admits "stage comparison relations" (on M), then it is closed under negation (on M).