The Craig interpolation theorem for prepositional logics with strong negation

Studia Logica ◽  
1985 ◽  
Vol 44 (3) ◽  
pp. 291-317 ◽  
Author(s):  
Valentin Goranko
Keyword(s):  
Interpolation Theorem ◽  
Strong Negation ◽  
Craig Interpolation

The Craig Interpolation Theorem

2012 ◽  
pp. 260-269
Author(s):  
George S. Boolos ◽  
John P. Burgess ◽  
Richard C. Jeffrey
Keyword(s):  
Interpolation Theorem ◽  
Craig Interpolation

Generalized interpolation theorems

1972 ◽  
Vol 37 (2) ◽  
pp. 343-351
Author(s):  
Stephen J. Garland
Keyword(s):  
Interpolation Theorem ◽  
Second Order ◽  
Cut Elimination ◽  
Real Numbers ◽  
Craig Interpolation ◽  
First Order ◽  
Order Variable ◽  
Analytic Sets ◽  
Image Position ◽  
Special Case

Chang [1], [2] has proved the following generalization of the Craig interpolation theorem [3]: For any first-order formulas φ and ψ with free first- and second-order variables among ν1, …, νn, R and ν1, …, νn, S respectively, and for any sequence Q1, …, Qn of quantifiers such that Q1 is universal whenever ν1 is a second-order variable, ifthen there is a first-order formula θ with free variables among ν1, …, νn such that(Note that the Craig interpolation theorem is the special case of Chang's theorem in which Q1, …, Qn are all universal quantifiers.) Chang also raised the question [2, Remark (k)] as to whether the Lopez-Escobar interpolation theorem [6] for the infinitary language Lω1ω possesses a similar generalization. In this paper, we show that the answer to Chang's question is affirmative and, moreover, that several interpolation theorems for applied second-order languages for number theory also possess such generalizations.Maehara and Takeuti [7] have established independently proof-theoretic interpolation theorems for first-order logic and Lω1ω which have as corollaries both Chang's theorem and its analog for Lω1ω. Our proofs are quite different from theirs and rely on model-theoretic techniques stemming from the analogy between the theory of definability in Lω1ω and the theory of Borel and analytic sets of real numbers, rather than the technique of cut-elimination.

scholarly journals Algebraic Characterization of the Local Craig Interpolation Property

2018 ◽  
Vol 47 (1) ◽  
Author(s):  
Zalán Gyenis
Keyword(s):  
Algebraic Logic ◽  
Interpolation Property ◽  
Interpolation Theorem ◽  
Algebraic Characterization ◽  
Local Version ◽  
Ongoing Research ◽  
Craig Interpolation ◽  
Craig Interpolation Property ◽  
Superamalgamation Property

The sole purpose of this paper is to give an algebraic characterization, in terms of a superamalgamation property, of a local version of Craig interpolation theorem that has been introduced and studied in earlier papers. We continue ongoing research in abstract algebraic logic and use the framework developed by Andréka– Németi and Sain. 

scholarly journals Localizing predicate activity in resolution proofs

2019 ◽  
Author(s):  
Marcello Sachs
Keyword(s):  
Structural Properties ◽  
Interpolation Theorem ◽  
Order Logic ◽  
First Order Logic ◽  
Constructive Proof ◽  
Craig Interpolation ◽  
First Order ◽  
Resolution Proofs

A theorem is proven regarding our ability to construct resolution proofs with certain structural properties. This theorem is then used to provide a new constructive proof of the Craig Interpolation Theorem for Classical First Order Logic.

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