Separating intermediate predicate logics of well-founded and dually well-founded structures by monadic sentences

2014 ◽  
Vol 25 (3) ◽  
pp. 527-547 ◽  
Author(s):  
A. Beckmann ◽  
N. Preining
Keyword(s):  
Intermediate Predicate Logics

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.

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.

On logics intermediate between intuitionistic and classical predicate logic

1959 ◽  
Vol 24 (2) ◽  
pp. 141-153 ◽  
Author(s):  
Toshio Umezawa
Keyword(s):  
Propositional Logic ◽  
Predicate Logic ◽  
Classical Propositional Logic ◽  
Intermediate Predicate Logics ◽  
Study Inclusion ◽  
Classical Predicate

In [1] and [2] I investigated logics intermediate between intuitionistic and classical propositional logic. In the present paper I shall study inclusion and non-inclusion between certain intermediate predicate logics. All the logics considered result from intuitionistic predicate logic by addition of classically valid axiom schemes.

On finite linear intermediate predicate logics

Studia Logica ◽  
1988 ◽  
Vol 47 (4) ◽  
pp. 391-399 ◽  
Author(s):  
Hiroakira Ono
Keyword(s):  
Intermediate Predicate Logics ◽  
Finite Linear
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