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1. Intermediate Logic
The Intermediate Logic module divides into two parts which are taught and assessed separately Classical Logic and Nonclassical logics.
http://www-users.york.ac.uk/~twcs1/Int Logic/index.htm
University of York Philosophy Department Current Students Prospective Students ... News
##### Autumn Term 2006
The Intermediate Logic module divides into two parts which are taught and assessed separately: Classical Logic and Non-classical Logics. Mastering Classical Logic is a necessary condition for understanding and evaluating non-classical logics.
• The teaching for this part consists of 9 lectures and 4 seminars. Procedural work consists in doing exercises for the seminars. Each week I will specify some exercises which you must complete (see below). However, you should aim to do all the exercises in the book in preparation for the exam. Assessment is by a 1 hour closed examination in Week 1, Spring 2007. This examination counts 1/3rd towards the module mark.
YOU MUST OWN YOUR OWN COPY OF LOGIC PRIMER by Colin Allen and Michael Hand by the FRIDAY OF WEEK 2. Otherwise you will not be able to follow this module. This book comes with a very useful online resource at: http://logic.tamu.edu/ . This includes a quiz for testing your knowledge and tools to check proofs. You woudl be very unwise not to take full advantage of this during the Christmas vacation. All logic textbook contain some errors. The errata for this book are listed at

2. On The Independent Axiomatizability Of Modal And Intermediate Logics -- CHAGROV
This paper gives a solution to the old independent axiomatizability problem by presenting normal modal logics above K4 and Grz and an Intermediate logic
http://logcom.oxfordjournals.org/cgi/content/abstract/5/3/287
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Oxford University Press

##### On the Independent Axiomatizability of Modal and Intermediate Logics
ALEXANDER CHAGROV and MICHAEL ZAKHARYASCHEV Tver State University Zhelyabova Str.33, Tver 170013, Russia.
Institute of Applied Mathematics Miusskaya Sq.4, Moscow 125047, Russia This paper gives a solution to the old independent axiomatizability problem by presenting normal modal logics above K4 and Grz and an intermediate logic without independent axiomatizations. Incidentally

 3. JSTOR On Intermediate Logics. Intermediate propositional logics are logics M such that L c M c LPx. Below we shall use logic for Intermediate propositional logic.http://links.jstor.org/sici?sici=0022-4812(197106)36:2<329:OIL>2.0.CO;2-K

4. A Study Of Intermediate Predicate Logics
12 Umezawa, T., On logics Intermediate between intuitionistic and classical 13 Gabbay, D. M., Applications of trees to Intermediate logics,
http://projecteuclid.org/handle/euclid.prims/1195192964
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##### A study of intermediate predicate logics
Hiroakira Ono Source: Publ. Res. Inst. Math. Sci. Volume 8, Number 3 (1972), 619-649. Primary Subjects: Full-text: Access granted (open access) PDF File (2116 KB) Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.prims/1195192964 Mathematical Reviews number (MathSciNet): Zentralblatt Math identifier: back to Table of Contents
##### References
[1] Church, A., Introduction to mathematical logic I, Princeton, N. J., 1956. Zentralblatt MATH: [2] Hosoi, T., On intermediate logics I,J. Fac. ScL, Univ. Tokyo, Sec.7, 14 (1967), 293-312. Mathematical Reviews (MathSciNet): Zentralblatt MATH: [3] Hosoi, T. and H. Ono, Intermediate prepositional logics (A survey), J. of Tsuda College, 5 (1973). Mathematical Reviews (MathSciNet): [4] Jankov, V. A., Constructing a sequence of strongly independent superintuitionistic propositional calculi, Soviet Math. Dokl, 9 (1968), 806-807.

5. CJO - Abstract - Characterization Of Strongly Equivalent Logic Programs In Inter
Characterization of strongly equivalent logic programs in Intermediate logics. DICK HJ DE JONGH, LEX HENDRIKS Theory and Practice of Logic Programming
http://journals.cambridge.org/abstract_S147106840200159X
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##### Cambridge Journals Online
Skip to content Theory and Practice of Logic Programming (2003), 3: 259-270 Cambridge University Press doi:10.1017/S147106840200159X Published online by Cambridge University Press 13May2003 Copy and paste this link: http://journals.cambridge.org/action/displayAbstract?aid=149964
##### Characterization of strongly equivalent logic programs in intermediate logics
DICK H. J. DE JONGH and LEX HENDRIKS
Institute of Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands (email: dickdj@science.uva.nl

6. Median Logic
Such logics are called Intermediate or superintuitionistic. Intermediate logics are usually defined by adding one or more axiom schemas weaker than LEM to
http://sakharov.net/median.html
Home Email Alexander Sakharov Irina ... Tim Projects Resources Sport Photos Median Logic Math Foundations Badminton Clubs Trip Photos ... Assertion Propagation
##### Median Logic
The question 'Which of the two logics - classical and intuitionistic - is better?' has been around for about a century. Each has certain advantages over the other in certain dimensions. Both intuitionistic and classical logic have issues, too. Classical logic has decent models but existence proofs are not constructive in it. Intuitionistic logic has disjunction and existence properties and thus constructive proofs but the propositional fragment of intuitionistic logic while being finite does not have a finite model. It seems that classical logic has a 'better' propositional part whereas intuitionistic logic is 'better' suited for purely predicate statements. Is it possible to combine the best of both worlds? Research in this domain was initiated by Godel and Tarski almost as soon as intuitionistic logic emerged. Since derivable intuitionistic formulas constitute a subset of derivable classical formulas, the focus of this research is on investigating properties of the logics lying between the two. Such logics are called intermediate or superintuitionistic. Intermediate logics are usually defined by adding one or more axiom schemas weaker than LEM to intuitionistic logic. I introduced a bizarre intermediate logic that coincides with classical logic in its propositional part and coincides with intuitionistic logic in its purely predicate part. This logic is closed under modus ponens and closed under propositional substitution. This logic is a minimal intermediate logic that coincides with classical logic in its propositional part and coincides with intuitionistic logic on the set of formulas not containing propositional symbols. The minimality of median logic is critical because it implies that no other extension covering classical propositional logic can be made more ÂintuitionisticÂ than median logic. Whereas supersets of median logic are less intuitionistic, its subsets are not fully classical in the propositional part.

7. CiNii - Kripke Models And Intermediate Logics
Kripke Models and Intermediate logics. ONO Hiroakira 1. 1Research Institute for Mathematical Sciences, Kyoto University. Read/Search Full Text. Holdings
http://ci.nii.ac.jp/naid/110001839698/en/
Top Page Browse Publications Citation Index CiNii+Citation Index ... Japanese Journal Title
##### Publications of the Research Institute for Mathematical Sciences
Vol.6, No.3(19710300) pp. 461-476 Kyoto University ISSN:00345318 Bibliography
##### ONO Hiroakira
[Research Institute for Mathematical Sciences, Kyoto University] Read/Search Full Text Holdings NII Article ID (NAID) NII NACSIS-CAT ID (NCID) Text Lang ENG Databases NII-ELS Export Refer/BibIX Format BibTex Format Tab Separated Text (TSV) NII HOME ... NII-REO National Institute of Informatics

8. Michael Kremer | The Department Of Philosophy | The University Of Chicago Divisi
We study some more advanced topics in logic, building on Intermediate Logic I. Possible topics include GÃ¶del s incompleteness theorems; higherorder logics
http://philosophy.uchicago.edu/faculty/kremer.html
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##### Michael Kremer
Michael Kremer is Professor of Philosophy. He received his PhD from the University of Pittsburgh in 1986. Prior to joining the University of Chicago department he taught at the University of Notre Dame for sixteen years. His chief research interests are in logic, philosophy of language, and early analytic philosophy. He also has a strong interest in issues concerning the relationship between reason and religious faith. CV ( RTF
##### Contact
office: Stuart Hall, Room 224
office phone: 773/834-9884
email: kremer@uchicago.edu
##### Selected Publications
• The Cardinal Problem of Philosophy, forthcoming in Wittgenstein and the Moral Life, A. Crary, ed. ( DOC Logicist Responses to Kant: (Early) Russell and (Early) Frege, forthcoming in Philosophical Topics ( PDF Sense and Meaning: The Origins and Development of the Distinction, forthcoming in the Cambridge Companion to Frege, T. Ricketts and M. Potter, eds. Review of Scott Soames, Philosophical Analysis in the Twentieth Century

 9. DMG-FG2: People Furthermore, I am interested in the particular features that distinguishes intuitionistic logic from classical logic or other Intermediate logics,http://www.dmg.tuwien.ac.at/fg2/index.php?id=19

10. DBLP: Mauro Ferrari
8 Agata Ciabattoni, Mauro Ferrari Hypertableau and PathHypertableau Calculi for Some Families of Intermediate logics. TABLEAUX 2000 160-174
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/f/Ferrari:Mauro.html
##### Mauro Ferrari
List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Alessandro Avellone , Mauro Ferrari, Camillo Fiorentini Guido Fiorino Ugo Moscato : ESBC: an application for computing stabilization bounds. Electr. Notes Theor. Comput. Sci. 153 EE Mario Ornaghi Marco Benini , Mauro Ferrari, Camillo Fiorentini Alberto Momigliano : A Constructive Object Oriented Modeling Language for Information Systems. Electr. Notes Theor. Comput. Sci. 153 EE Mauro Ferrari, Camillo Fiorentini Guido Fiorino : On the complexity of the disjunction property in intuitionistic and modal logics. ACM Trans. Comput. Log. 6 EE Mauro Ferrari, Camillo Fiorentini Guido Fiorino : A secondary semantics for Second Order Intuitionistic Propositional Logic. Math. Log. Q. 50 EE Mauro Ferrari, Pierangelo Miglioli Mario Ornaghi : On Uniformly Constructive and Semiconstructive Formal Systems. Logic Journal of the IGPL 11 Mauro Ferrari, Camillo Fiorentini : A Proof-theoretical Analysis of Semiconstructive Intermediate Theories. Studia Logica 73 EE Mauro Ferrari

11. , Vol. 37(51), Pp. 7--15, 1985
Abstract We give semantics for Intermediate logics of the form $H+\vee S$, where $\vee S$ is the schema $$\underset{(i,j)\in S}\to\vee(A_i\to A_j)$$ and
http://www.emis.de/journals/PIMB/051/2.html
Vol. 37(51), pp. 715 (1985) Previous Article Next Article Contents of this Issue Other Issues ... EMIS Home
##### Semantics for some intermediate logics
Abstract: Classification (MSC2000): Full text of the article:
ELibM
for the EMIS Electronic Edition

12. M. Zakharyaschev: Research Papers
On the independent axiomatizability of modal and Intermediate logics. Journal of Logic and Modal companions of Intermediate propositional logics.
http://www.dcs.bbk.ac.uk/~michael/papers1.html
##### Research papers and books
• A. Artale, D. Calvanese, R. Kontchakov, V. Ryzhikov and M. Zakharyaschev. Reasoning over Extended ER Models. Accepted for ER'07. Paper A. Artale, D. Calvanese, R. Kontchakov and M. Zakharyaschev. Query Answering in Expressive Variants of DL-Lite. Proceedings of the Fifteenth Italian Symposium on Advanced Database Systems (SEBD 2007, Torre Canne, Fasano, Italy, June 17-20, 2007), pp. 250-257, 2007. Paper R. Kontchakov, F. Wolter and M. Zakharyaschev. Modularity in DL-Lite. Proceedings of DL'07 (Brixen/Bressanone, Italy, June 8-10, 2007), pp. 76-87, 2007. CEUR Workshop Proceedings, vol. 250. Paper A. Artale, D. Calvanese, R. Kontchakov, V. Ryzhikov and M. Zakharyaschev. Complexity of Reasoning over Entity-Relationship Models. Proceedings of DL'07 (Brixen/Bressanone, Italy, June 8-10, 2007), pp. 163-170, 2007. CEUR Workshop Proceedings, vol. 250. Paper A. Artale, R. Kontchakov, C. Lutz, F. Wolter and M. Zakharyaschev. Temporalising tractable description logics. In V. Goranko and X.S. Wang, editors, Proceedings of TIME 2007 (Alicante, Spain, June 28-30, 2007), pp. 11-22. IEEE Computer Society, 2007. Paper A. Artale, D. Calvanese, R. Kontchakov, and M. Zakharyaschev.
• 13. Springer Online Reference Works
The most natural way of specifying Intermediate logics is by Intermediate The set of all Intermediate logics is a lattice under the inclusion relation
http://eom.springer.de/I/i051880.htm
 Encyclopaedia of Mathematics I Article referred from Article refers to Intermediate logic of propositions, propositional intermediate logic An arbitrary consistent set of propositional formulas that is closed under the derivation rule modus ponens and the substitution rule , and that contains all axioms of intuitionistic propositional calculus The most natural way of specifying intermediate logics is by intermediate propositional calculi. Each such calculus is given by adding a certain number of classical generally-valid propositional formulas to the axioms of The set of all intermediate logics is a lattice under the inclusion relation , and the finitely-axiomatizable intermediate logics form a sublattice in it, in which every finite distributive lattice can be isomorphically imbedded. An intermediate logic is called solvable if there is an algorithm that, for any propositional formula , recognizes whether does or does not belong to . Thus, classical and intuitionistic logic are both solvable. In general, any finitely-approximated (cf. below) finitely-axiomatizable intermediate logic is solvable. An example of a finitely-axiomatizable unsolvable intermediate logic has been constructed (cf. An intermediate logic is called disjunctive if implies that or . Intuitionistic logic, e.g., has this property, but classical logic does not. There is an infinite number of disjunctive intermediate logics.

14. Dr. Marcus Kracht: Publications In Mathematics
On Extensions of Intermediate logics by Strong Negation , Journal of Philosophical Logic 27(1998), 49 73. Simulation and Transfer Results in Modal Logic
http://www.linguistics.ucla.edu/people/Kracht/html/public-math.html
Publications in Mathematics
##### Books and Lecture Notes
• " (2001, in German) Tools and Techniques in Modal Logic ", Studies in Logic and the Foundations of Mathematics No. 142, Elsevier, Amsterdam, 1999.
• ##### Articles
• Elementary Models for Modal Predicate Logics, Part 2: Modal Individuals Revisited ", in Reinhard Kahle (ed.): "Intensionality", 2005, 60 - 96. (with Oliver Kutz). Notes On Substitution in First-Order Logic ", in: Vincent Hendricks, Fabian Neuhaus, Stig-Andur Pedersen, Uwe Scheffler, Heinrich Wansing (eds.): First-Order Logic Revisited , Logos Verlag, Berlin, 2004, 155 - 172. Notes on the Space Requirements for Checking Satisfiability in Modal Logics ", IN: Philippe Balbiani, Nobo-Yuki Suzuki, Frank Wolter and Michael Zakaryaschev (eds.): Advances in Modal Logic 4 , King's College Publications, 2003, 243 - 264. "Invariant Logics", Mathematical Logic Quarterly 48(2002), 29 - 50. "Atomic Incompleteness of how to kill one bird with two stones", Bulletin of Section Logic 30/2(2001), 71 - 78. "Elementary Models for Modal Predicate Logic. Part I: Completeness", in: F. Wolter, M. de Rijke, H. Wansing, and M. Zakharyaschev (eds.): Proceedings of AiML 2000 (with Oliver Kutz).
• 15. Intuitionistic And Intermediate Logics In CoS
Hi, I am currently working on formalizing intuitionistic and Intermediate logics (Dummett s LC and firstorder Goedel logic) in CoS.
http://osdir.com/ml/science.mathematics.frogs/2006-05/msg00001.html
##### Intuitionistic and intermediate logics in CoS
Subject Intuitionistic and intermediate logics in CoS Hi, I am currently working on formalizing intuitionistic and intermediate logics (Dummett's LC and first-order Goedel logic) in CoS. I have a draft paper written; if any of you happen to be working on the same thing, or are interested, please let me know and I can send the paper to you. You can find the abstract below. Best, -Alwen A local system for intuitionistic logic Abstract: This paper presents systems for first-order intuitionistic logic and several of its extensions in which all the propositional rules are local, in the sense that, in applying the rules of the system, one needs only a fixed amount of information about the logical expressions involved. The main source of non-locality is the contraction rules. We show that the contraction rules can be restricted to the atomic ones, provided we employ deep inference, i.e., to allow rules to apply anywhere inside logical expressions. We further show that the use of deep

16. Intermediate Logics And Factors Of The Medvedev Lattice
Intermediate logics and factors of the Medvedev lattice. Authors, Sorbi, Andrea; Terwijn, Sebastiaan A. Publication, eprint arXivmath/0606494
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We investigate the initial segments of the Medvedev lattice as Brouwer algebras, and study the propositional logics connected to them. Bibtex entry for this abstract Preferred format for this abstract (see Preferences
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 17. Hypersequent Calculi For Some Intermediate Logics With Bounded Kripke Models Hypersequent Calculi for some Intermediate logics with Bounded Kripke Models. Agata Ciabattoni. Journal Title Journal of Logic and Computation. Date 2001http://wotan.liu.edu/docis/show?doc=dbl/joloco/2001_11_2_283_HCFSIL.htm&query=

18. Rosalie Iemhoff
Properties of Intuitionistic Provability and Preservativity logics. COMBLOG 04, Logic Journal of the IGPL 13 (6), 2005. ps. R. Iemhoff. Intermediate logics
http://www.phil.uu.nl/~iemhoff/papers.html
##### Publications
M. Baaz and R. Iemhoff. Konstruktivismus und Intuitionismus. (German)
Internationale Mathematische Nachrichte 150, Oesterreich, 2006. ps S. Artemov and R. Iemhoff. The basic intuitionistic logic of proofs.
Journal of Symbolic Logic , 72 (2), 2007 (p. 439-451). ps M. Baaz and R. Iemhoff. On the Skolemization of existential quantifiers in intuitionistic logic.
Annals of Pure and Applied Logic , 142 (1-3), 2006 (p.269-295). ps M. Baaz and R. Iemhoff. On the proof theory of the existence predicate.
We will show them! Essays in honour of Dov Gabbay , S. Artemov, H. Barringer, A. Garcez, L. Lamb and J. Woods (editors), King's College Publications, 2005. ps M. Baaz and R. Iemhoff. On interpolation in existence logics.
Proceedings LPAR 2005 , Lecture Notes in Computer Science 3835, 2005 (697-711). ps M. Baaz and R. Iemhoff. Gentzen calculi for the existence predicate.
Studia Logica , 82 (1), 2006 (p.7-23). ps R.Iemhoff. A note on linear Kripke models.
Journal of Logic and Computation , 15 (4), 2005 (p. 489-506).

19. TABLEAUX 2005
Parallel versions of Lorenzen s game and corresponding hypersequent systems for Intermediate logics. Dialogue games as models of distributed proof search.
http://tableaux2005.uni-koblenz.de/tutorials.html
##### All tutorials will be held in parallel
Tutorial 1 Instance Based Methods The term 'instance based methods' (IBM) refers to a family of methods for first-order logic theorem proving. IBMs share the principle of carrying out proof search by maintaining a set of instances of input clauses and analyzing it for satisfiability until completion. IBMs are conceptually essentially different to well established methods like resolution or free-variable analytic tableaux. Also, IBMs exhibit a search space and termination behaviour (in the satisfiable case) different from those methods, which makes them attractive from a practical point of view as a complementary method. This observation is also supported empirically by results obtained with the first serious implementations available (carried out by Letz and Stenz, cf. the system competitions (CASC) at CADE-18 and CADE-19). The idea behind IBMs is already present in a rudimentary way in the work by Davis, Putnam, Logemann and Loveland in the early sixties. The contemporary stream of research on IBMs was initiated with the Plaisted's Hyperlinking calculus in 1992. Since then, other methods have been developed by Plaisted and his coworkers. Billon's disconnection calculus was picked up by Letz and Stenz and has been significantly developed further since then. New methods have also been introduced by Hooker, Baumgartner and Tinelli, and more recently by Ganzinger and Korovin. The stream of publications over the last years demonstrates a growing interest in IBMs. The ideas presented there show that research on IBMs still is in the middle of development, and that there is high potential further improvements and extensions like equality and theory handling, which is currently investigated.

 20. Citebase - Characterization Of Strongly Equivalent Logic Programs In Intermediat (1999) Duplicationfree tableau calculi and related cut-free sequent calculi for the interpolable propositional Intermediate logics. Logic Journal of thehttp://www.citebase.org/abstract?identifier=oai:arXiv.org:cs/0206005&action=cite

 21. Scientific Commons Computable Kripke Models And Intermediate We investigate e ectiveness of completeness by Kripke results for Intermediate logics such as for example, intuitionistic logic, classical logic,http://en.scientificcommons.org/314637

22. Duplication-free Tableau Calculi And Related Cut-free Sequent Calculi For The In
We get cutfree sequent calculi for the interpolable propositional Intermediate logics by translating suitable duplication-free tableau calculi developed
http://jigpal.oxfordjournals.org/cgi/content/abstract/7/4/447
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Oxford University Press

##### Duplication-free tableau calculi and related cut-free sequent calculi for the interpolable propositional intermediate logics
A Avellone M Ferrari and P Miglioli We get cut-free sequent calculi for the interpolable propositional intermediate logics by translating suitable duplication-free tableau calculi developed within a semantical framework. From this point of view, the paper also provides semantical proofs of the admissibility of the cut-rule for appropriate cut-free sequent calculi.

23. Www.vlsi-world.com - State Machine Encoding (Gray, Binary And One-hot)
This kind of state coding avoids Intermediate logics. For example if a sate wants to change itÂs state from 01 to 10 . Here both bits are getting changed
http://www.vlsi-world.com/content/view/42/34/
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HDL VHDL Examples State machine encoding (Gray, Binary and One-hot) State machine encoding (Gray, Binary and One-hot) Save this page Page 1 of 4 Each state of a state machine can be represented with a unique pattern of high (1) and low (0) register output signals, this process called "encoding." The two primary encoding methods are binary and one-hot encoding.
One-hot encoding uses one flip-flop for each state. For example if there are 10 states in logic then it will use 10 flip-flops. This type of encoding is fast because only one bit needed to check for each state. It implies complex logic and more area inside the chip due to more number of flip-flops. Check the following one hot encoded state values (for a 4 state state-machine)
Gray encoding (a type of binary encoding) is especially useful when the outputs of the state bits are used asynchronously. This kind of state coding avoids intermediate logics. For example if a sate wants to change it’s state from "01" to "10". Here both bits are getting changed, in reality both flip-flops will not change at the same time. So there are two possibilities for this transition. Check this following diagram for the two possible transitions. Now it is clear that there is an intermediate state exits while state transitioning. If any logic reads this state variable asynchronously then output will be unpredictable. This intermediate logic avoided by using gray code. In Gray coding; between state transitions only one bit will change. See the following gray state values there is only one bit is changing during state transition. This completely eliminates intermediate states.

24. [Author] Alexander Sakharov [Title] Median Logic [AMS Subj-class
Author Alexander Sakharov Title Median logic AMS Subjclass 03B55 Intermediate logics 03B20 Subsystems of classical logic Abstract Median logic
http://www.mathsoc.spb.ru/preprint/2004/04-12.txt
 [Author] Alexander Sakharov [Title] Median logic [AMS Subj-class] 03B55 Intermediate logics 03B20 Subsystems of classical logic [Abstract] Median logic introduced here is a minimal intermediate logic that combines classical properties in its propositional part and intuitionistic properties for derivations not containing propositional symbols. A sequent calculus and other formulations are presented for median logic. Cut elimination is proven for the sequent calculus formulation. Constrained Kripke structures are introduced for modeling median logic. The extent of the disjunction and existence properties is investigated. [Keywords] intermediate logic, classical logic, intuitionistic logic, sequent calculus, cut elimination, Kripke structures, disjunction property, existence property [Comments] LaTeX, English, 20 pp. [Contact e-mail] alex@sakharov.net

25. Intermediate Logics (logic) - Philosophy Dictionary And Research Guide
Intermediate logics In mathematical logic, an Intermediate logic (also called superintuitionistic) is a propositional logic extend.
http://www.123exp-beliefs.com/t/00804286309/
The Language of Philosophy - Dictionary and Research Guide Provided by
##### Intermediate logics
In mathematical logic, an intermediate logic (also called superintuitionistic) is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent intermediate logic, whence the name (the logics are intermediate between intuitionistic and classical logics).
##### Wikipedia and Wikis

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Last update: December 19, 2007

26. British Library Direct: Order Details
Order from the British Library On the rules of Intermediate logics.
http://direct.bl.uk/research/54/39/RN189636075.html

27. Mauro Ferrari
On the complexity of disjunction and explicit definability properties in some Intermediate logics. In LPAR 2002 Logic for Programming Artificial
http://www.dicom.uninsubria.it/~ferram/publications/
Mauro Ferrari - Publications - By topic Indice
##### Intuitionistic and intermediate logics
M. Ferrari, C. Fiorentini, and G. Fiorino. On the complexity of the disjunction property in intuitionistic and modal logics. ACM, TOCL
Abstract
ACM Transactions on Computational Logic(TOCL)
M. Ferrari, C. Fiorentini, and G. Fiorino. A secondary semantics for second order intuitionistic propositional logic. Mathematical Logic Quarterly
Abstract
In this paper we propose a Kripke-style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics.
M. Ferrari and C.Fiorentini. A proof-theoretical analysis of semiconstructive intermediate theories. Studia Logica
Abstract
In the 80's Pierangelo Miglioli, starting from motivations in the framework of Abstract Data Types and Program Synthesis, introduced semiconstructive theories, a family of large subsystems'' of classical theories that guarantee the computability of functions and predicates represented by suitable formulas. In general, the above computability results are guaranteed by algorithms based on a recursive enumeration of the theorems of the whole system. In this paper we present a family of semiconstructive systems, we call

 28. A Sequence Of Decidable Finitely Axiomatizable Intermediate Logics rdfslabel, A Sequence of Decidable Finitely Axiomatizable Intermediate logics with the Disjunction Property. (xsdstring). swrcnumber, 1 (xsdstring)http://dblp.l3s.de/d2r/resource/publications/journals/jsyml/GabbayJ74

29. DI & CoS - Current Research Topics And Open Problems
Intermediate logics It should be possible, and probably rather easy, to present in CoS some Intermediate logics like Corsi s logic and GÃ¶del s logic.
http://alessio.guglielmi.name/res/cos/crt.html
Alessio Guglielmi's Research Deep Inference and the Calculus of Structures / Current Research Topics and Open Problems
##### Deep Inference and the Calculus of Structures Current Research Topics and Open Problems
In this page I list all open and currently explored research subjects I am aware of, in the area of deep inference and closely related matters. The solutions to most of these problems are instrumental in reaching the common goal of a comprehensive bureaucracy-free proof theory based on geometric methods.
##### Contents
• Introduction Calculus of Structures
• Calculus of structures without involutive negation Designing term calculi for systems in the calculus of structures ...
##### Introduction
In very few words, what we do is looking for the best syntax and the best semantics for proofs (notice that semantics of proofs is a very different thing from semantics of formulae!). It is necessary to improve on the current state of the art in structural proof theory in order to solve important open problems like that of identity of proofs . By employing deep inference, which yields the necessary flexibility for the task, we are making very fast progress.
• 30. Welcome To The JANCL Web Site
Nonclassical logics cover a large variety of formalisms such as modal logics, temporal logics, epistemic logics, conditional logics, Intermediate logics,
http://www.irit.fr/JANCL/
##### Journal of Applied Non-Classical Logics
JANCL webpage ) which aims at promoting the development of non-classical logics in Computer Science, with contributions ranging from mathematical foundations of such logics to their applications in Computer Science. Non-classical logics cover a large variety of formalisms such as: modal logics, temporal logics, epistemic logics, conditional logics, intermediate logics, non-monotonic logics, logics of vagueness, logics of uncertainty, relevance logics, paraconsistent logics, multivalued logics, logics of programs, etc. The following areas, among others, are relevant for the Journal of Applied Non-Classical Logics:
• Formal aspects of non-classical formalisms (completeness, decidability, complexity...) Applications of non-classical logics to:
Artificial Intelligence and Cognitive Science (knowledge representation, automated reasoning, natural language,...) Theoretical Computer Science (program verification, program synthesis...)
Applications to other domains are welcome if they illustrate the usefulness of non-classical logics. The journal is published four times a year (twice a year before 1996) with regular papers describing original work or high quality synthesis work, short research notes, position papers, a problem section, information about meetings and conferences, call for papers, and book reviews. Contacts: Journal of Applied Non-Classical Logics Webm@ster Last update: June 21, 2006

31. Intermediate Logic - Wikipedia, The Free Encyclopedia
In mathematical logic, an Intermediate logic (also called superintuitionistic) is a propositional logic extending intuitionistic logic.
http://en.wikipedia.org/wiki/Intermediate_logics
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##### Intermediate logic
(Redirected from Intermediate logics Jump to: navigation search In mathematical logic , an intermediate logic (also called superintuitionistic ) is a propositional logic extending intuitionistic logic Classical logic is the strongest consistent intermediate logic, whence the name (the logics are intermediate between intuitionistic logic and classical logic). There exists a continuum of different intermediate logics. Specific intermediate logics are often constructed by adding one or more axioms to intuitionistic logic, or by a semantical description. Examples of intermediate logics include:
• intuitionistic logic ( IPC Int IL H classical logic ( CPC Cl CL IPC + P Ã¢ÂÂ¨ ÃÂ¬P the logic of the weak excluded middle KC Jankov 's logic, De Morgan logic): IPC + ÃÂ¬ÃÂ¬P Ã¢ÂÂ¨ ÃÂ¬P GÂ¶del Dummett logic ( LC G IPC + (P Ã¢ÂÂ Q) Ã¢ÂÂ¨ (Q Ã¢ÂÂ P) Kreisel Putnam logic: IPC + (ÃÂ¬P Ã¢ÂÂ (Q Ã¢ÂÂ¨ R)) Ã¢ÂÂ ((ÃÂ¬P Ã¢ÂÂ Q) Ã¢ÂÂ¨ (ÃÂ¬P Ã¢ÂÂ R)) Medvedev 's logic of finite problems ( LM or ML realizability logics Scott 's logic: IPC + ((ÃÂ¬ÃÂ¬P Ã¢ÂÂ P) Ã¢ÂÂ (P Ã¢ÂÂ¨ ÃÂ¬P)) Ã¢ÂÂ (ÃÂ¬ÃÂ¬P Ã¢ÂÂ¨ ÃÂ¬P) Smetanich's logic: IPC + (ÃÂ¬Q Ã¢ÂÂ P) Ã¢ÂÂ (((P Ã¢ÂÂ Q) Ã¢ÂÂ P) Ã¢ÂÂ P)
The tools for studying intermediate logics are similar to those used for intuitionistic logic, such as

 32. Intermediate Logic Student Textbook 2nd Edition Expanded, Corrected, Completely Redesigned New Edition! This is the textbook used in the 2nd semester of 8th grade at Logos School, taught by James Nance,http://www.logosschool.com/materials/shop/item.asp?itemid=82

33. Intermediate Logic
This class is a study of the language of firstorder logic (FOL). One reason to study FOL is the intrinsic interest of the central concept it is built to
http://www3.baylor.edu/~Todd_Buras/Intermediate Logic-06.htm
Todd Buras courses papers events ... links
Contact Information Morrison Hall 224 Phone: 254-710-7338 Todd_Buras@baylor.edu
##### Phil: 4345Intermediate Logic
Fall 2006 course information course description course objectives course requirements ... graduate section meetings Course Information Instructor: Todd Buras
Office: MH 224
Office Hours: MWF 10-12, TTH 8-9.30, and by appointment
Phone: 710-7338 (office); 752-0169 (home)
e-mail: Todd_Buras@baylor.edu Required Text: John Barwise and John Etchemendy, Language, Proof and Logic (CSLI Publications). A note on the text: You will need the textbook and the software package that comes with it. DO NOT buy a used copy of this text . What you are paying for is the registration ID for the software, which is only good for one user. So a used copy will be of no use to you (and you should not expect to get much for your used copy). Believe me, the use of this software is worth paying for! back to top Course Description This class is a study of the language of first-order logic (FOL). One reason to study FOL is the intrinsic interest of the central concept it is built to study: consequence.

34. Intermediate Logic
This course goes beyond an introduction to logic and deals not merely with the formal mechanics of proving validity, soundness, consistency,
http://www.humboldt.edu/~mfg1/web315.html

35. Atlas: Non-finite Axiomatizability Of The Intermediate Logic Of Chequered Subset
The Intermediate logic Cheq corresponds to the modal logic of chequered subsets of R , i.e. finite unions of products of convex subsets of R, introduced by
http://atlas-conferences.com/cgi-bin/abstract/caug-46
 Atlas home Conferences Abstracts about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL'07) August 5-9, 2007 St Anne's College, University of Oxford Oxford, England Organizers Mai Gehrke and Hilary Priestley View Abstracts Conference Homepage Non-finite axiomatizability of the intermediate logic of chequered subsets of R by Timofei Shatrov Moscow State University The intermediate logic Cheq corresponds to the modal logic of chequered subsets of R , i.e. finite unions of products of convex subsets of R , introduced by van Benthem et al. in their paper "Euclidean Hierarchy in Modal Logic" (2003). Recently, there were several publications concerning this logic, but the question of the possibility of its finite axiomatization remained unanswered. We prove that Cheq is not axiomatizable in finite number of variables, answering this question. PDF Date received: May 12, 2007 Atlas Conferences Inc. Document # caug-46.

36. [cs/0206005] Characterization Of Strongly Equivalent Logic Programs In Intermedi
In this paper we will show that KC (the logic obtained by adding axiom ~A v ~~A to intuitionistic logic), is the weakest Intermediate logic for which
http://arxiv.org/abs/cs.LO/0206005
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##### Title: Characterization of Strongly Equivalent Logic Programs in Intermediate Logics
Authors: Dick de Jongh Lex Hendriks (Submitted on 3 Jun 2002) Abstract: The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of 'strong equivalence' between logical programs that can be verified in 3-valued Goedel logic, G3, the strongest non-classical intermediate propositional logic (Lifschitz, Pearce and Valverde, 2001). In this paper we will show that KC (the logic obtained by adding axiom ~A v ~~A to intuitionistic logic), is the weakest intermediate logic for which strongly equivalent logic programs, in a language allowing negations, are logically equivalent. Comments: Under consideration for publication in Theory and Practice of Logic Programming Subjects: Logic in Computer Science (cs.LO)

37. IngentaConnect The Unique Intermediate Logic Whose Every Rule Is Archetypal
In this paper we provide a proof of this conjecture and show that it is the unique Intermediate logic with this property. Keywords Rules of inference,
http://www.ingentaconnect.com/content/oup/igpl/2005/00000013/00000003/art00269;j
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##### The Unique Intermediate Logic Whose Every Rule is Archetypal
Author: Source: Logic Journal of the IGPL , Volume 13, Number 3, May 2005 , pp. 269-275(7) Publisher: Oxford University Press Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: Informally, we can say that an inference rule is archetypal if any other rule can be transformed to it (up to suitable equivalence) via some substitution for the propositional variables. It was shown by L. Humberstone that, in the case of classical propositional logic, every non-degenerate binary rule is archetypal and conjectured that this result holds also for all rules in the full language. In this paper we provide a proof of this conjecture and show that it is the unique intermediate logic with this property.

 38. Characterization Of Strongly Equivalent Logic Programs In Intermediate Logics In this paper we will show that KC (the logic obtained by adding axiom $\neg A\vee\neg\neg A$ to intuitionistic logic), is the weakest Intermediate logichttp://portal.acm.org/citation.cfm?id=986819.986820&dl=GUIDE&dl=GUIDE&CFID=15151

39. Department Of Computer Science - Deep Inference Systems For Intuitionistic And I
I will further show that the use of deep inference allows for modular extensions of intuitionistic logic to Dummett s Intermediate logic LC, Goedel logic
http://www.cs.bath.ac.uk/department/logic-seminar/deep-inference-systems-for-int
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Deep Inference Systems for Intuitionistic and Intermediate Logics
##### Dr Alwen Tiu Australian National University
University of Bath Wednesday 30th May
##### Abstract:
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 40. Intermediate Logic: Student First, in order to present to the student a more logical progression of topics, the section on defining terms has been moved from Intermediate Logic tohttp://www.canonpress.org/shop/item.asp?itemid=1048

41. Intuitionistic Logic (Stanford Encyclopedia Of Philosophy)
An Intermediate propositional logic is any consistent collection of propositional formulas containing all the axioms of IPC and closed under modus ponens
http://plato.stanford.edu/entries/logic-intuitionistic/
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