Linear Kripke frames and Gödel logics

2007 ◽  
Vol 72 (1) ◽  
pp. 26-44 ◽  
Author(s):  
Arnold Beckmann ◽  
Norbert Preining
Keyword(s):  
Kripke Frame ◽  
Gödel Logic ◽  
Kripke Frames ◽  
Intermediate Predicate Logics ◽  
Constant Domains ◽  
Complete Characterisation

AbstractWe investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countable linear Kripke frames with constant domains: We obtain a complete characterisation of axiomatisability of logics based on countable linear Kripke frames with constant domains. Furthermore, we obtain that the total number of logics defined by countable linear Kripke frames on constant domains is countable.

Intermediate predicate logics determined by ordinals

1990 ◽  
Vol 55 (3) ◽  
pp. 1099-1124 ◽  
Author(s):  
Pierluigi Minari ◽  
Mitio Takano ◽  
Hiroakira Ono
Keyword(s):  
Predicate Logic ◽  
The Other ◽  
Constant Domain ◽  
Kripke Frames ◽  
Other Hand ◽  
Countable Ordinal ◽  
Intermediate Predicate Logics ◽  
Regular Ordinal

AbstractFor each ordinal α > 0, L(α) is the intermediate predicate logic characterized by the class of all Kripke frames with the poset α and with constant domain. This paper will be devoted to a study of logics of the form L(α). It will be shown that for each uncountable ordinal of the form α + η with a finite or a countable η(> 0), there exists a countable ordinal of the form β + η such that L(α + η) = L(β + η). On the other hand, such a reduction of ordinals to countable ones is impossible for a logic L(α) if α is an uncountable regular ordinal. Moreover, it will be proved that the mapping L is injective if it is restricted to ordinals less than ωω, i.e. α ≠ β implies L(α) ≠ L(β) for each ordinal α, β ≤ ωω.

scholarly journals Kripke Incompleteness of First-order Calculi with Temporal Modalities of CTL and Near Logics

2015 ◽  
Vol 21 (1) ◽  
pp. 86-99
Author(s):  
Е. А. Котикова ◽  
М. Н. Рыбаков
Keyword(s):  
Temporal Logic ◽  
Expressive Power ◽  
Branching Time ◽  
First Order ◽  
Kripke Frames ◽  
Order Language ◽  
Constant Domains ◽  
Kripke Incompleteness ◽  
Computational Tree Logic

We study an expressive power of temporal operators used in such logics of branching time as computational tree logic or alternating-time temporal logic. To do this we investigate calculi in the first-order language enriched with the temporal operators used in such logics. We show that the resulting languages are so powerful that many ‘natural’ calculi in the languages are not Kripke complete; for example, if a calculus in such language is correct with respect to the class of all serial linear Kripke frames (even just with constant domains) then it is not Kripke complete. Some near questions are discussed.

scholarly journals A Finite Model Property for Gödel Modal Logics

10.29007/vgh2 ◽  
2018 ◽  
Author(s):  
Xavier Caicedo ◽  
George Metcalfe ◽  
Ricardo Rodriguez ◽  
Jonas Rogger
Keyword(s):  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
First Order ◽  
Gödel Logic ◽  
Np Completeness ◽  
Kripke Frames ◽  
The One

A new semantics with the finite model property is provided and used to establish decidability for Gödel modal logics based on (crisp or fuzzy) Kripke frames combined locally with Gödel logic. A similar methodology is also used to establish decidability, indeed co-NP-completeness, for a Gödel S5 logic that coincides with the one-variable fragment of first-order Gödel logic.

scholarly journals Bi-modal Godel logic over [0,1]-valued Kripke frames

2012 ◽  
Vol 25 (1) ◽  
pp. 37-55 ◽  
Author(s):  
X. Caicedo ◽  
R. O. Rodriguez
Keyword(s):  
Gödel Logic ◽  
Kripke Frames

scholarly journals An Algebraic Study of S5-Modal Gödel Logic

Studia Logica ◽  
2021 ◽  
Author(s):  
Diego Castaño ◽  
Cecilia Cimadamore ◽  
José Patricio Díaz Varela ◽  
Laura Rueda
Keyword(s):  
Gödel Logic

scholarly journals On the correspondence between nested calculi and semantic systems for intuitionistic logics

2020 ◽  
Author(s):  
Tim Lyon
Keyword(s):  
Intuitionistic Logic ◽  
Structural Rules ◽  
First Order ◽  
Constant Domains ◽  
The Relationship ◽  
Intuitionistic Logics

Abstract This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics.

scholarly journals Bispecific antibodies with Fab-arms featuring exchanged antigen-binding constant domains

2021 ◽  
Vol 26 ◽  
pp. 100959
Author(s):  
Filippo Benedetti ◽  
Florian Stracke ◽  
Gerhard Stadlmayr ◽  
Katharina Stadlbauer ◽  
Florian Rüker ◽  
...  
Keyword(s):  
Binding Constant ◽  
Bispecific Antibodies ◽  
Antigen Binding ◽  
Constant Domains
Sign in / Sign up

Export Citation Format

Share Document