scholarly journals Undecidable problems for modal definability: Table 1.

2016 ◽  
pp. exv094
Author(s):  
Philippe Balbiani ◽  
Tinko Tinchev
Keyword(s):  
Modal Definability

scholarly journals Notes on modal definability.

1988 ◽  
Vol 30 (1) ◽  
pp. 20-35 ◽  
Author(s):  
Johan van Benthem
Keyword(s):  
Modal Definability

On the Modal Definability of Simulability by Finite Transitive Models

Studia Logica ◽  
2011 ◽  
Vol 98 (3) ◽  
pp. 347-373 ◽  
Author(s):  
David Fernández Duque
Keyword(s):  
Modal Definability

scholarly journals Characterising modal definability of team-based logics via the universal modality

2019 ◽  
Vol 170 (9) ◽  
pp. 1100-1127
Author(s):  
Katsuhiko Sano ◽  
Jonni Virtema
Keyword(s):  
Modal Definability

A new proof of Sahlqvist's theorem on modal definability and completeness

1989 ◽  
Vol 54 (3) ◽  
pp. 992-999 ◽  
Author(s):  
G. Sambin ◽  
V. Vaccaro
Keyword(s):  
Modal Logic ◽  
Personal Computer ◽  
Topological Spaces ◽  
Straightforward Manner ◽  
Original Proof ◽  
Complete Proof ◽  
Modal Formula ◽  
First Order ◽  
Modal Definability ◽  
General Frames

There are not many global results on modal logics. One of these is the following theorem by Sahlqvist on completeness and correspondence for a wide class of modal formulae (including many well known logics, e.g. D, T, B, S4, K4, S5, …) (see [S]).Sahlqvist's Theorem. Let A be any modal formula which is equivalent to a conjunction of formulae of the form □m(A1 → A2), where m ≥ 0, A2 is positive and A1 is obtained from propositional variables and their negations applying ∧, ∨, ♢, and □ in such a way that no positive occurrence of a variable is in a subformula of the form B1 ∨ B2 or ♢ B1 within the scope of some □. Then A corresponds effectively to a first order formula, and L + A is canonical whenever Lis a canonical logic.A formula A satisfying the above conditions is henceforth called a Sahlqvist formula. Unfortunately, till now, the only complete proof was the original proof of Sahlqvist (a proof of the correspondence half has also been given by van Benthem [vB]). It is so complicated and long that even in an advanced textbook of modal logic [HC] it has not found a place. Here, by considering general frames as topological spaces, an attitude which we developed in [TD], we give a proof of Sahlqvist's theorem simplified to such an extent that one can easily grasp the key idea on which it is based and apply the resulting algorithm to specific modal formulae in a straightforward manner, suitable even for implementation on a personal computer. This key idea also improves on previous preliminary work in the same direction (see [S1], [S2]).

scholarly journals Modal definability of first-order formulas with free variables and query answering

2013 ◽  
Vol 11 (2) ◽  
pp. 190-216 ◽  
Author(s):  
Stanislav Kikot ◽  
Evgeny Zolin
Keyword(s):  
Query Answering ◽  
First Order ◽  
Free Variables ◽  
Modal Definability

scholarly journals Modal definability in enriched languages.

1989 ◽  
Vol 31 (1) ◽  
pp. 81-105 ◽  
Author(s):  
Valentin Goranko
Keyword(s):  
Modal Definability

Branching-time logic with quantification over branches: The point of view of modal logic

1996 ◽  
Vol 61 (1) ◽  
pp. 1-39 ◽  
Author(s):  
Alberto Zanardo
Keyword(s):  
Modal Logic ◽  
Second Order ◽  
Point Of View ◽  
Branching Time ◽  
First Order ◽  
Kripke Structures ◽  
Time Logic ◽  
The Moment ◽  
Modal Definability ◽  
Or History

AbstractIn Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as ‘at some branch, or history (passing through the moment at hand)’. Both the bundled-trees semantics [Burgess 79] and the 〈moment, history〉 semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (3-modal) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames.

scholarly journals Modal Definability Based on Łukasiewicz Validity Relations

Studia Logica ◽  
2016 ◽  
Vol 104 (2) ◽  
pp. 343-363
Author(s):  
Bruno Teheux
Keyword(s):  
Modal Definability
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