Translating inaccessible worlds logic into bimodal logic

2005 ◽  
pp. 145-150 ◽  
Author(s):  
Olivier Gasquet ◽  
Andreas Herzig
Keyword(s):  
Bimodal Logic

scholarly journals Bimodal Logic with the Irreflxive Modality

2007 ◽  
Vol 34 (1) ◽  
pp. 1-10 ◽  
Author(s):  
KATSUHIKO SANO ◽  
YASUO NAKAYAMA
Keyword(s):  
Bimodal Logic

scholarly journals Disappearing Diamonds: Fitch-Like Results in Bimodal Logic

2019 ◽  
Vol 48 (6) ◽  
pp. 1003-1016
Author(s):  
Weng Kin San
Keyword(s):  
Bimodal Logic

scholarly journals Properties of independently axiomatizable bimodal logics

1991 ◽  
Vol 56 (4) ◽  
pp. 1469-1485 ◽  
Author(s):  
Marcus Kracht ◽  
Frank Wolter
Keyword(s):  
Deep Understanding ◽  
Finite Model ◽  
Finite Model Property ◽  
Large Classes ◽  
Modal Operators ◽  
Bimodal Logic ◽  
Bimodal Logics ◽  
Modal Systems ◽  
Transfer Theorems ◽  
Polymodal Logic

In monomodal logic there are a fair number of high-powered results on completeness covering large classes of modal systems; witness for example Fine [74], [85] and Sahlqvist [75]. Monomodal logic is therefore a well-understood subject in contrast to polymodal logic, where even the most elementary questions concerning completeness, decidability, etc. have been left unanswered. Given that in many applications of modal logic one modality is not sufficient, the lack of general results is acutely felt by the “users” of modal logics, contrary to logicians who might entertain the view that a deep understanding of one modality alone provides enough insight to be able to generalize the results to logics with several modalities. Although this view has its justification, the main results we are going to prove are certainly not of this type, for they require a fundamentally new technique. The results obtained are called transfer theorems in Fine and Schurz [91] and are of the following type. Let L ∌ ⊥ be an independently axiomatizable bimodal logic and L⎕ and L∎ its monomodal fragments. Then L has a property P iff L⎕ and L∎ have P. Properties which will be discussed are completeness, the finite model property, compactness, persistence, interpolation and Halldén-completeness. In our discussion we will prove transfer theorems for the simplest case when there are just two modal operators, but it will be clear that the proof works in the general case as well.

scholarly journals Knowing-How under Uncertainty (Extended Abstract)

2020 ◽  
Author(s):  
Pavel Naumov ◽  
Jia Tao
Keyword(s):  
Modal Logics ◽  
Logical System ◽  
Epistemic Modal ◽  
Knowing How ◽  
Know How ◽  
Bimodal Logic

Logical systems containing knowledge and know-how modalities have been investigated in several recent works. Independently, epistemic modal logics in which every knowledge modality is labeled with a degree of uncertainty have been proposed. This article combines these two research lines by introducing a bimodal logic containing knowledge and know-how modalities, both labeled with a degree of uncertainty. The main technical results are soundness, completeness, and incompleteness of the proposed logical system with respect to two classes of semantics.

Epistemic Entrenchment in Autoepistemic Logic

1992 ◽  
Vol 17 (1-2) ◽  
pp. 5-29
Author(s):  
Craig Boutilier
Keyword(s):  
Epistemic Entrenchment ◽  
Autoepistemic Logic ◽  
Equal Status ◽  
Bimodal Logic ◽  
Belief Set

A drawback of existing epistemic logics is their inability to deal with entrenchment of beliefs. All beliefs have equal status; none can be held more firmly than others. We present a bimodal logic that generalizes Levesque’s reconstruction of autoepistemic logic. In our system standard epistemic concepts can be represented, including the notion of only knowing, but elements of a belief set may be more or less entrenched. This has important implications for the distinction between epistemic defaults and subjunctive (and normative) defaults, both of which are representable in our system.

scholarly journals A Basic System of Congruential-to-Monotone Bimodal Logic and Two of Its Extensions

1996 ◽  
Vol 37 (4) ◽  
pp. 602-612
Author(s):  
I. L. Humberstone
Keyword(s):  
Basic System ◽  
Bimodal Logic

Bimodal Logic

2012 ◽  
Vol 6 (2) ◽  
pp. 71-93
Author(s):  
Daniel Rönnedal ◽  
Keyword(s):  
Bimodal Logic

scholarly journals Erdős Graphs Resolve Fine's Canonicity Problem

2004 ◽  
Vol 10 (2) ◽  
pp. 186-208 ◽  
Author(s):  
Robert Goldblatt ◽  
Ian Hodkinson ◽  
Yde Venema
Keyword(s):  
Chromatic Number ◽  
Boolean Algebras ◽  
Finite Graphs ◽  
Boolean Algebras With Operators ◽  
First Order ◽  
Relational Structures ◽  
Bimodal Logic ◽  
Simulation Results ◽  
Large Chromatic Number ◽  
Standing Question

AbstractWe show that there exist 2ℵ0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results of Thomason). The constructions use the result of Erdos that there are finite graphs with arbitrarily large chromatic number and girth.

Noncompactness in propositional modal logic

1972 ◽  
Vol 37 (4) ◽  
pp. 716-720 ◽  
Author(s):  
S. K. Thomason
Keyword(s):  
Modal Logic ◽  
Predicate Logic ◽  
Expressive Power ◽  
Second Order ◽  
Order Logic ◽  
Relational Models ◽  
Propositional Modal Logic ◽  
Bimodal Logic ◽  
Deductive Power ◽  
Second Order Logic

We have come to believe that propositional modal logic (with the usual relational semantics) must be understood as a rather strong fragment of classical second-order predicate logic. (The interpretation of propositional modal logic in second-order predicate logic is well known; see e.g. [2, §1].) “Strong” refers of course to the expressive power of the languages, not to the deductive power of formal systems. By “rather strong” we mean sufficiently strong that theorems about first-order logic which fail for second-order logic usually fail even for propositional modal logic. Some evidence for this belief is contained in [2] and [3]. In the former is exhibited a finitely axiomatized consistent tense logic having no relational models, and the latter presents a finitely axiomatized modal logic between T and S4, such that □p → □2p is valid in all relational models of the logic but is not a thesis of the logic. The result of [2] is strong evidence that bimodal logic is essentially second-order, but that of [3] does not eliminate the possibility that unimodal logic only appears to be incomplete because we have not adopted sufficiently powerful rules of inference. In the present paper we present stronger evidence of the essentially second-order nature of unimodal logic.

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