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Intuitionistic axiomatizations for bounded extension Kripke models

Mohammad Ardeshir, Wim Ruitenburg, Saeed Salehi
2003 Annals of Pure and Applied Logic  
As examples we present an axiom system for the class of coÿnal extension Kripke models, and an axiom system for the class of end-extension Kripke models.  ...  We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model.  ...  Acknowledgements We would like to thank Bardia Hesam for his useful comments, Mojtaba Moniri and Morteza Moniri for helpful discussions, and Hiroakira Ono for sending us his paper [7] .  ... 
doi:10.1016/s0168-0072(03)00058-7 fatcat:qz3qtsbxczha7nqyobcvetxzou

An Independence Result for Intuitionistic Bounded Arithmetic

Morteza Moniri
2006 Journal of Logic and Computation  
the chain as a 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|).  ...  For the definition of Kripke models of intuitionistic bounded arithmetic and basic results about them, see [M2] and [B2] .  ... 
doi:10.1093/logcom/exi085 fatcat:gxdlsvxk6fgjbnegws5ua7ap74

Comparing Constructive Arithmetical Theories Based on NP-PIND and coNP-PIND

M. Moniri
2003 Journal of Logic and Computation  
Similar results hold also for length induction in place of polynomial induction. We also investigate the relation between various other intuitionistic first-order theories of bounded arithmetic.  ...  Our method is mostly semantical, we use Kripke models of the theories. 2000 Mathematics Subject Classification: 03F30, 03F55, 03F50, 68Q15.  ...  I would like to thank two anonymous referees for suggestions that led to improvements in the presentation of the paper. This research was in part supported 8 by a grant from IPM.  ... 
doi:10.1093/logcom/13.6.881 fatcat:six76ujd45ajhprhoq7t4trxfm

ℋ-theories, fragments of HA and PA -normality

Morteza Moniri
2002 Archive for Mathematical Logic  
For a classical theory T , H(T ) denotes the intuitionistic theory of T -normal (i.e. locally T ) Kripke structures. S.  ...  We show P A-normality of once-branching Kripke models of HA + M P , where it is not known whether the same holds if M P is dropped. 1991 Mathematics Subject Classification: 03F55, 03F30.  ...  Proposition 2.4 (i) Any reversely well founded end-extension Kripke model of iop is Iop-normal. (ii) Any linear Kripke model of iop + M P open is Iop-normal.  ... 
doi:10.1007/s001530200008 fatcat:vreaokp6p5awrbxi23swa24azi

Page 6723 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
extension Kripke models.  ...  Ex- amples presented are an axiom system for the class of cofinal extension Kripke models and an axiom system for the class of end-extension Kripke models.  ... 

On Model Theory for Intuitionistic Bounded Arithmetic with Applications to Independence Results [chapter]

Samuel R. Buss
1990 Feasible Mathematics  
Our model theory for IPV and IPV + is a strengthening of the usual Kripke semantics for intuitionistic first-order logic: we consider Kripke structures in which each "world" is a classical model of CPV  ...  Section 5 contains the completeness theorem for IPV + with respect to CPV-normal Kripke models.  ...  The corresponding semantic notion for intuitionistic first-order logic is that of a Kripke model.  ... 
doi:10.1007/978-1-4612-3466-1_3 fatcat:zanrwcwjwrcsvcibt4s4mopuyq

Some weak fragments of HA and certain closure properties

Morteza Moniri, Mojtaba Moniri
2002 Journal of Symbolic Logic (JSL)  
On the other hand, we prove that iop is equivalent with the intuitionistic theory axiomatized by PA − plus the scheme of weak ¬¬ LNP for open formulas, where universal quantification on the parameters  ...  We include some remarks on the classical worlds in Kripke models of iop.  ...  Also, ¬¬iΠ 1 will stand for the intuitionistic theory axiomatized by i∆ 0 + {¬¬I x ϕ : ϕ ∈ Π 1 }.  ... 
doi:10.2178/jsl/1190150031 fatcat:fjk7xr7v7jf7lcl5mrlcfkwtre

A Semantic Approach to Conservativity

Tomasz Połacik
2016 Studia Logica: An International Journal for Symbolic Logic  
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.  ...  In particular, we describe a class 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  ...  For the background, axiomatization and properties of CZF see [8, 10] . In general, constructing Kripke models for a particular intuitionistic theory is a difficult task.  ... 
doi:10.1007/s11225-015-9639-7 fatcat:ac3wgrynqzfv7p2enoj5x2lwia

Page 1688 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
The upper bound is shown by exhibiting a tree structure of the models.  ...  We first prove completeness for the logics with respect to Kripke models; then we trace the correspondence between Kripke models and topo- logical spaces that have been enhanced with an explicit notion  ... 

Quantifier Elimination for a Class of Intuitionistic Theories

Ben Ellison, Jonathan Fleischmann, Dan McGinn, Wim Ruitenburg
2008 Notre Dame Journal of Formal Logic  
While one can always "unravel" a functor Kripke model to obtain a partial order Kripke model with the same intuitionistic theory, our technique is perhaps an easier way to consider a Kripke model that  ...  For a given JRS theory in a language with nullary predicates, we construct a model that is in some sense universal.  ...  Hc for the intuitionistic theory axiomatized by Hc1 through Hc4.  ... 
doi:10.1215/00294527-2008-012 fatcat:no7bphghjzgafaxuu7yrh52soi

On classical behavior of intuitionistic modalities

Sergey Drobyshevich
2014 Logic and Logical Philosophy  
We investigate which basic compositions, i.e. compositions of the form ¬δ, δ¬ or ¬δ¬, yield modal operators of the same type over intuitionistic logic as over classical logic.  ...  We study connections between four types of modal operators  necessity, possibility, un-necessity and impossibility  over intuitionitstic logic in terms of compositions of these modal operators with intuitionistic  ...  As usual non-trivial extensions of intuitionistic logic we will call superintuitionistic logics. Let us define Heyting-Kripke logics.  ... 
doi:10.12775/llp.2014.019 fatcat:5dvymv455rgwhozbjjw3ggzfaq

The Unintended Interpretations of Intuitionistic Logic [chapter]

Wim Ruitenburg
2008 Perspectives on the History of Mathematical Logic  
We conclude with remarks on the quest for a correct interpretation of intuitionistic logic.  ...  We present an overview of the unintended interpretations of intuitionistic logic that arose after Heyting formalized the "observed regularities" in the use of formal parts of language, in particular, first-order  ...  I want to thank John Simms and Paul Bankston for many helpful comments and suggestions for improvement.  ... 
doi:10.1007/978-0-8176-4769-8_10 fatcat:irsbmrq63bfztnrdlascelcguy

A Variant of Thomason's First-Order Logic CF Based on Situations

Xuegang Wang, Peter Mott
1998 Notre Dame Journal of Formal Logic  
For the logic CF 0 , the usual Kripke formal semantics is de ned based on situations, and a sound and complete axiomatic system is established based on the axiomatic systems of constructive logics with  ...  With the use of bounded quanti ers, CF 0 allows the domain of quanti cation to be empty and allows for non-denoting constants. CF 0 is intended as a fragment of a logic for situation theory.  ...  His semantical model is a hybrid of a Kripke model for propositional intuitionistic logic (as the conditional is intuitionistic) and a classical model for predicate logic (as the universal quanti er is  ... 
doi:10.1305/ndjfl/1039293021 fatcat:x2iqkbckt5ehholvwv2rnlhfea

Page 1417 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
Classical model-theoretic results often imply intuitionistic model- theoretic results, because Kripke models are first-order definable.  ...  Merrie Bergmann (1-SMTH-C; Northampton, MA) 97¢:03033 03B20 03C90 Dzierzgowski, Daniel (B-UCL; Louvain-la-Neuve) Constants in Kripke models for intuitionistic logic. (English summary) Math.  ... 

Page 2324 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
We show how several standard timing analyses can be characterised as algorithms computing correct and exact stabil- isation bounds for particular PST timing models.  ...  We introduce hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the fi- nite model property.  ... 
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