Journal ArticleDOI
Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actually” Operators
TLDR
This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing “actually” operators, the weakest of which are conservative extensions of K, using a novel generalisation of the standard semantics.Abstract:
The addition of “actually” operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing “actually” operators has concentrated entirely upon extensions of KT5 and has employed a particular model-theoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing “actually” operators, the weakest of which are conservative extensions of K, using a novel generalisation of the standard semantics.read more
Citations
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Journal ArticleDOI
Deciding Regular Grammar Logics with Converse Through First-Order Logic
Stéphane Demri,Hans de Nivelle +1 more
TL;DR: In this paper, a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic, was given.
Journal ArticleDOI
Free choiceness and non-individuation
Jacques Jayez,Lucia M. Tovena +1 more
TL;DR: It is shown that under certain conditions, FCIs can occur in episodic, non-modal sentences, a fact that NI can accommodate, and more fine-grained aspects of the semantics of FCIs, such as their emotional colour.
Posted Content
Deciding regular grammar logics with converse through first-order logic
Stéphane Demri,Hans de Nivelle +1 more
TL;DR: The results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators.
Journal ArticleDOI
Two-dimensional adventures
TL;DR: The authors recall some applications of modal logic from the 1980s, including work on the logic of 'Actually' and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity.
Journal ArticleDOI
Actuality, necessity, and logical truth'
TL;DR: The authors discusses and refutes Zalta's argument in the context of a language for propositional modal logic with an actuality connective, and shows that the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language connective for deep necessity.
References
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Book
An Introduction to Modal Logic
Max J. Cresswell,G. E. Hughes +1 more
TL;DR: This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic with all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing clarity of exposition and approachability.
Book
Modal Logic: An Introduction
TL;DR: This chapter discusses standard models for modal logics, classical systems of modal logic, and Determination and decidability for classical systems.