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Decidable Kripke models of intuitionistic theories

1998
*
Annals of Pure and Applied Logic
*

In this paper we introduce effectiveness into

doi:10.1016/s0168-0072(97)00057-2
fatcat:7febp3f57bdyjecvq5sz6bnzta
*model**theory**of**intuitionistic*logic. ... The main result shows that any computable*theory*T*of**intuitionistic*predicate logic has a*Kripke**model*with decidabIe forcing such that for any sentence 4, 4 is forced in the*model*if and only if C$ is ... Acknowledgements T is complete for the class*of*We would like to thank the referee for valuable comments on improvements*of*the paper. ...##
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A Semantic Approach to Conservativity

2016
*
Studia Logica: An International Journal for Symbolic Logic
*

In particular, we describe a class

doi:10.1007/s11225-015-9639-7
fatcat:ac3wgrynqzfv7p2enoj5x2lwia
*of*formulae for which such conservativity results can be proven in case*of*any*intuitionistic**theory*T which is complete with respect to a class*of*T-normal*Kripke**models*... We also prove conservativity results for*intuitionistic**theories*which are closed under the Friedman translation and complete with respect to a class*of*conversely well-founded*Kripke**models*. ... Let us note that not every T c -normal*Kripke**model*is a*model**of*the*intuitionistic**theory*T i . Also, a*Kripke**model**of*a*theory*T i need not be T c -normal. ...##
###
Computable Kripke Models and Intermediate Logics

1998
*
Information and Computation
*

We introduce effectiveness considerations into

doi:10.1006/inco.1998.2704
fatcat:kjwfg7am4rcmnjlxamvxe3btde
*model**theory**of**intuitionistic*logic. ... We proceed by looking in detail at how one went from*model**theory**of*classical first-order logic to*model**theory**of**intuitionistic*logic. ... Every computable*intuitionistic**theory*T is complete for the class*of**decidable**Kripke**models*. ...##
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Comparing Constructive Arithmetical Theories Based on NP-PIND and coNP-PIND

2003
*
Journal of Logic and Computation
*

Our method is mostly semantical, we use

doi:10.1093/logcom/13.6.881
fatcat:six76ujd45ajhprhoq7t4trxfm
*Kripke**models**of*the*theories*. 2000 Mathematics Subject Classification: 03F30, 03F55, 03F50, 68Q15. ... In this note we show that the*intuitionistic**theory**of*polynomial induction on Π b+ 1 -formulas does not imply the*intuitionistic**theory*IS 1 2*of*polynomial induction on Σ b+ 1 -formulas. ... Acknowledgements Final version*of*this paper to appear in the Journal*of*Logic and Computation. ...##
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Some remarks on the complexity of Henkin-Kripke models

1978
*
Indagationes Mathematicae (Proceedings)
*

An interesting corollary to be drawn immediately from this observation is the following: a

doi:10.1016/1385-7258(78)90047-1
fatcat:2kdvh4pqqndrzcisj2qpxrnqx4
*decidable**intuitionistic**theory*has a recursive*Kripke**model*; and for*decidable**intuitionistic**theories*completeness ... (i)*of*the preceding theorem is the exact*intuitionistic*analogue*of*the well-known classical result that consistent*decidable**theories*have recursive*models*, and improves on theorem 1 on page 84*of*[ ...##
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An Independence Result for Intuitionistic Bounded Arithmetic

2006
*
Journal of Logic and Computation
*

the chain as a

doi:10.1093/logcom/exi085
fatcat:gxdlsvxk6fgjbnegws5ua7ap74
*Kripke**model*. ... It is shown that the*intuitionistic**theory**of*polynomial induction on positive Π b 1 (coNP) formulas does not prove the sentence ¬¬∀x, y∃z ≤ y(x ≤ |y| → x = |z|). ... Corollary 2.3 Suppose K is a weak end extension*Kripke**model*whose accessibility relation is ω and*decides*atomic formulas. ...##
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Some weak fragments of HA and certain closure properties

2002
*
Journal of Symbolic Logic (JSL)
*

We include some remarks on the classical worlds in

doi:10.2178/jsl/1190150031
fatcat:fjk7xr7v7jf7lcl5mrlcfkwtre
*Kripke**models**of*iop. ... This is established by constructing a*Kripke**model**of*iop + ¬L y (2y > x), where L y (2y > x) is universally quantified on x. ... The*intuitionistic**theory**of*the class*of*T -normal*Kripke*structures is denoted H(T ). It was shown in [AM, 1.2(ii, iii), 1.4, 2.3(ii) ] that*Kripke**models**of*lop (resp. ...##
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Some remarks on the complexity of Henkin-Kripke models

1978
*
Indagationes Mathematicae (Proceedings)
*

An int erest ing corollary to be drawn immediately from this observation is the following : a

doi:10.1016/s1385-7258(78)80020-1
fatcat:7rs6qiskzbaxhj3qnyra4zmgka
*decidable**intuitionistic**theory*has a recursive*Kripke**model*; and for*decidable**intuitionistic**theories*completeness ... If we apply the method*of*proof*of*theorem A to an r.e.*theory*r (instead*of*a*decidable**theory*) we find the following PROPOSITION. ...##
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Intuitionistic weak arithmetic

2003
*
Archive for Mathematical Logic
*

We construct ω-framed

doi:10.1007/s00153-003-0189-8
fatcat:nmvgu6p24zefhko3vkqruoiizu
*Kripke**models**of*i∀ 1 and iΠ 1 non*of*whose worlds satisfies ∀x∃y(x = 2y ∨ x = 2y + 1) and ∀x, y∃zExp(x, y, z) respectively. ... A formula ϕ(x) is*decidable*in a*Kripke**model*K whenever K ∀x(ϕ(x) ∨ ¬ϕ(x)). For a set T*of*sentences, T i and T c denote its*intuitionistical*and classical deductive closures. ... By [K, P. 69] , each node*of*this*Kripke**model*is a ∆ o -elementary substructure*of*M (therefore*models*Π 1 -*theory*I∆ 0 ) and non*of*them satisfies exp. ...##
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Page 568 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

He calls the

*models*ancestral*Kripke**models*, inductive ancestral*Kripke**models*, and nonhereditary*Kripke**models*, respectively, and proves that with respect to each*of*these classes the Heyting propositional ... (NL-AMST-PR) The expressive force*of*some fragments*of**intuitionistic*propositional logic with regard to*Kripke*frames. Z. Math. Logik Grundlag. Math. 37 (1991), no. 4, 357-362. ...##
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Page 4622 of Mathematical Reviews Vol. , Issue 2002G
[page]

2002
*
Mathematical Reviews
*

Define % to be a submodel

*of*the*Kripke**model*# if % can be obtained from # by removing nodes. Main Theorem: Let T C U be first-order*theories*. ... Then the class*of**Kripke**models**of*U is closed under all submodels that are*models**of*T if and only if U is axiomatizable by T plus a set*of*semipositive sentences. ...##
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Preservation theorems for bounded formulas

2006
*
Archive for Mathematical Logic
*

We show that, if the

doi:10.1007/s00153-006-0016-0
fatcat:jqbplx6rgncjpbdi2ibi4hw53m
*intuitionistic**theory**of*polynomial induction on strict Π b 2 formulas proves*decidability**of*Σ b 1 formulas, then P = NP. ... These results provide simple proofs for some known results in the*model**theory**of*the bounded arithmetic*theories*like CPV and PV 1 . ... For a semantical investigation*of*this*theory*, see [M1] , where*Kripke**models**of**intuitionistic*bounded arithmetic is studied. ...##
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Intuitionisitic Tableau Extracted
[chapter]

1999
*
Lecture Notes in Computer Science
*

This paper presents a formalization

doi:10.1007/3-540-48754-9_11
fatcat:wnznurcr4rf5pbneanbhpqhaau
*of*a sequent presentation*of*intuitionisitic propositional logic and proof*of**decidability*. ... If the argument to the resulting decision procedure is a valid sequent, a formal proof*of*that fact is returned, otherwise a counter-example in the form*of*a*Kripke*Countermodel is returned. ... With the proof*of**decidability*as our focus, we describe the formal development*of*a sequent proof*theory*, the tableau construction, and a formal*theory**of**Kripke*counter-examples which are used here as ...##
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Indefinite Reasoning with Definite Rules

1991
*
International Joint Conference on Artificial Intelligence
*

As a remedy, we propose the use

dblp:conf/ijcai/McCartyM91
fatcat:2ecufuexqncd5bc2crpgjbrjyy
*of*circumscribed definite rules, and we then investigate the proof*theory**of*this more expressive framework. ... circumscribed*theories*that are not equivalent to any first order*theory*. ... R has a final*Kripke**model*, which we denote by K*. ...##
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Page 5245 of Mathematical Reviews Vol. , Issue 91J
[page]

1991
*
Mathematical Reviews
*

V. (2-KRAS)
Admissibility

*of*inference rules with parameters in*intuitionistic*logic, and*intuitionistic**Kripke**models*. (Russian) Dokl. Akad. ... Since the algorithm uses exclusively*intuitionistic*means because it depends only on the properties*of*n-characteristic*Kripke**models*, the result can be considered as providing a solution to Problem 40 ...
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