Citations of:
Modal definability in enriched languages
Notre Dame Journal of Formal Logic 31 (1):81105 (1989)
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Propositional dynamic logic is one of the most successful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, as longknown, reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of (...) 

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names"  a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...) 



Viewing the language of modal logic as a language for describing directed graphs, a natural type of directed graph to study modally is one where the nodes are sets and the edge relation is the subset or superset relation. A wellknown example from the literature on intuitionistic logic is the class of Medvedev frames $\langle W,R\rangle$ where $W$ is the set of nonempty subsets of some nonempty finite set $S$, and $xRy$ iff $x\supseteq y$, or more liberally, where $\langle W,R\rangle$ (...) 

ABSTRACT George Gargov was an active pioneer in the ‘Sofia School’ of modal logicians. Starting in the 1970s, he and his colleagues expanded the scope of the subject by introducing new modal expressive power, of various innovative kinds. The aim of this paper is to show some general patterns behind such extensions, and review some very general results that we know by now, 20 years later. We concentrate on simulation invariance, decidability, and correspondence. What seems clear is that ‘modal logic’ (...) 

We describe a relational framework that uniformly supports formalization and automated reasoning in varied propositional modal logics. The proof system we propose is a relational variant of the classical RasiowaSikorski proof system. We introduce a compact graphbased representation of formulae and proofs supporting an efficient implementation of the basic inference engine, as well as of a number of refinements. Completeness and soundness results are shown and a Prolog implementation is described. 

Adam Brandenburger and H. Jerome Keisler have recently discovered a two person Russellstyle paradox. They show that the following configurations of beliefs is impossible: Ann believes that Bob assumes that Ann believes that Bob’s assumption is wrong. In [7] a modal logic interpretation of this paradox is proposed. The idea is to introduce two modal operators intended to represent the agents’ beliefs and assumptions. The goal of this paper is to take this analysis further and study this paradox from the (...) 

We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for complete axiomatization of the modal logics determined by a large family of classes of structures of any signature. 

Following the theory of Boolean algebras with modal operators , in this paper we investigate Boolean algebras with sufficiency operators and mixed operators . We present results concerning representability, generation by finite members, first order axiomatisability, possession of a discriminator term etc. We generalise the classes BAO, SUA, and MIA to classes of algebras with the families of relative operators. We present examples of the discussed classes of algebras that arise in connection with reasoning with incomplete information. 

We consider some modal languages with a modal operator $D$ whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at. 

ABSTRACT George Gargov was an active pioneer in the ‘Sofia School’ of modal logicians. Starting in the 1970s, he and his colleagues expanded the scope of the subject by introducing new modal expressive power, of various innovative kinds. The aim of this paper is to show some general patterns behind such extensions, and review some very general results that we know by now, 20 years later. We concentrate on simulation invariance, decidability, and correspondence. What seems clear is that ‘modal logic’ (...) 

