What is the upper part of the lattice of bimodal logics?

Studia Logica ◽  
1994 ◽  
Vol 53 (2) ◽  
pp. 235-241 ◽  
Author(s):  
Frank Wolter
Keyword(s):  
Bimodal Logics

Non-finitely axiomatisable two-dimensional modal logics

2012 ◽  
Vol 77 (3) ◽  
pp. 970-986 ◽  
Author(s):  
Agi Kurucz ◽  
Sérgio Marcelino
Keyword(s):  
Modal Logics ◽  
Two Dimensional ◽  
Recursively Enumerable ◽  
Bimodal Logics

AbstractWe show the first examples of recursively enumerable (even decidable) two-dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.

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.

Bimodal Logics for Reasoning About Continuous Dynamics

2002 ◽  
pp. 91-111 ◽  
Author(s):  
JEN M. DAVOREN ◽  
RAJEEV P. GORÉ
Keyword(s):  
Bimodal Logics

Bimodal logics for extensions of arithmetical theories

1996 ◽  
Vol 61 (1) ◽  
pp. 91-124 ◽  
Author(s):  
Lev D. Beklemishev
Keyword(s):  
Decision Procedures ◽  
Modal Logics ◽  
Kripke Semantics ◽  
Recursively Enumerable ◽  
Propositional Constants ◽  
Bimodal Logics ◽  
Natural Classes

AbstractWe characterize the bimodal provability logics for certain natural (classes of) pairs of recursively enumerable theories, mostly related to fragments of arithmetic. For example, we shall give axiomatizations, decision procedures, and introduce natural Kripke semantics for the provability logics of (IΔ0 + EXP, PRA); (PRA, IΣn); (IΣm, IΣn) for 1 ≤ m < n; (PA, ACA0); (ZFC, ZFC + CH); (ZFC, ZFC + ¬CH) etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants.

Rosser Orderings in Bimodal Logics

1989 ◽  
Vol 35 (4) ◽  
pp. 343-358 ◽  
Author(s):  
Alessandra Carbone ◽  
Franco Montagna
Keyword(s):  
Bimodal Logics

scholarly journals The Good, the Bad and the Right: Formal Reductions among Deontic Concepts

2021 ◽  
Author(s):  
Daniela Glavaničová ◽  
Matteo Pascucci
Keyword(s):  
Present Article ◽  
Moral Values ◽  
Taxonomic Analysis ◽  
The Right ◽  
Bimodal Logics

The present article provides a taxonomic analysis of bimodal logics of normative ideality and normative awfulness, two notions whose meaning is here explained in terms of the moral values pursued by a given community. Furthermore, the article addresses the problem of defining other relevant normative notions, such as obligation, explicit permission and Hohfeldian relations, in terms of ideality and awfulness. Some proposals formulated in the literature are improved and discussed with reference to the various logics introduced.

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