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A deterministic terminating sequent calculus for Godel-Dummett logic
1999
Logic Journal of the IGPL
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We give a short proof-theoretic treatment of a terminating contraction-free calculus G4-LC for the zero-order G odel-Dummett logic LC. ...
In our calculus, all the rules of G4-LC are invertible, thus allowing a deterministic proof-search procedure. ...
Acknowledgments We thank both Klaus Weich and Pierangelo Miglioli (and the latter's colleagues) for unpublished papers ( 24] , 1], 2]) and Klaus Weich and Sara Negri for helpful discussions. ...
doi:10.1093/jigpal/7.3.319
fatcat:vso2qfia7fc2thvlbcqwzjcyga
A Lambda Calculus for Gödel–Dummett Logic Capturing Waitfreedom
[chapter]
2012
Lecture Notes in Computer Science
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We propose a typed lambda calculus based on Avron's hypersequent calculus for Gödel-Dummett logic. This calculus turns out to model waitfree computation. ...
The calculus is not only proof theoretically interesting, but also valuable as a basis for distributed programming languages. ...
This work is encouraged by feedbacks from ACAN (Algebraic and Coalgebraic Approaches to Non-Classical Logics Workshop) and OPLSS'11 participants, supported by Grant-in-Aid for JSPS Fellows 23-6978, and ...
doi:10.1007/978-3-642-29822-6_14
fatcat:bmt6blzkmnbx7bdsf45laba7cu
Combining Proof-Search and Counter-Model Construction for Deciding Gödel-Dummett Logic
[chapter]
2002
Lecture Notes in Computer Science
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We present an algorithm for deciding Gödel-Dummett logic. ...
The originality of this algorithm comes from the combination of proofsearch in sequent calculus, which reduces a sequent to a set of pseudoatomic sequents, and counter-model construction of such pseudo-atomic ...
Gödel-Dummett logic LC In this section, we present the propositional Gödel-Dummett logic LC, its algebraic semantics, and some admissible sequent calculus rules, including the contraction-free system G4 ...
doi:10.1007/3-540-45620-1_7
fatcat:oac5c2ipjzfjtnk5aml4fdx5di
Counter-Model Search in Gödel-Dummett Logics
[chapter]
2004
Lecture Notes in Computer Science
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We present a new method for deciding Gödel-Dummett logic LC. ...
In section 5, we show that proof-search can be viewed as a non-deterministic choice of arrows in a bi-colored graph corresponding to left or right premises of proof-rules. ...
Then, we propose a new system for counter-model search in LC and LC n , mainly based on the notion of r-cycles in conditional graphs, and thus an efficient algorithm to decide these logics and provide ...
doi:10.1007/978-3-540-25984-8_19
fatcat:rjroafs3yjavtbkttzpcn2btye
Fast decision procedure for propositional Dummett logic based on a multiple premise tableau calculus
2010
Information Sciences
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We present a procedure to decide propositional Dummett logic. Such a procedure relies on a tableau calculus with a multiple premise rule and optimizations. ...
For this reason another name for the logic under consideration is Gödel-Dummett Logic. ...
We quote [8] for a throughout treatment of the subject. In the late '90 were presented tableau [1, 11] and sequent calculi [10] for propositional Dummett logic. ...
doi:10.1016/j.ins.2010.06.004
fatcat:jtlgbhvbrfbddhbsoysmdcqmzu
Hypertableau and Path-Hypertableau Calculi for some Families of Intermediate Logics
[chapter]
2000
Lecture Notes in Computer Science
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These calculi are obtained by adding one more structural rule to the path-hypertableau calculus for Intuitionistic Logic. ...
Using pathhypertableaux we define analytic calculi for the intermediate logics Bd k , with k ≥ 1, which are semantically characterized by Kripke models of depth ≤ k. ...
For instance, in [1] duplication-free tableau calculi for Sm, LQ and G ∞ have been defined (see also [10] for a deterministic terminating sequent calculus for G ∞ ). ...
doi:10.1007/10722086_15
fatcat:fuzurxaihnedth2ib2fob2qkdq
Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic
2008
Journal of Logic and Computation
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We present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. ...
Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. ...
We would like to thank Alwen Tiu for providing useful comments and suggestions, and pointing out errors in a draft of this paper. ...
doi:10.1093/logcom/exn067
fatcat:yxlmeg6y6zehxcxxgtxcopujza
Proofs and Countermodels in Non-Classical Logics
2014
Logica Universalis
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A method is presented that makes it possible to establish completeness in a direct way: For any given sequent either a proof in the given logical system or a countermodel in the corresponding frame class ...
Finitizations for intuitionistic propositional logic are obtained through the search for a minimal derivation, through pruning of infinite branches in search trees by means of a suitable syntactic counterpart ...
The famous modal translation * of intuitionistic logic was defined in a note by Gödel [Gödel, 1933] together with a syntactic proof that the translation is sound, namely that Int A implies S4 A * . ...
doi:10.1007/s11787-014-0097-1
fatcat:yzxgrtllgrga5j3nsc4qm5hgoy
Mathematical modal logic: A view of its evolution
[chapter]
2006
Handbook of the History of Logic
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This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. ...
It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. ...
For such assistance I thank Wim Blok, Max Cresswell, John Dawson, Allen Emerson, Saul Kripke, Neil Leslie, Ed Mares, Robin Milner, Hiroakira Ono, Lawrence Pedersen, Vaughan Pratt, Colin Stirling and Paul ...
doi:10.1016/s1874-5857(06)80027-0
fatcat:dihvhmx5vjhdjndl7x5auvqbki
Mathematical modal logic: A view of its evolution
2003
Journal of Applied Logic
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This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. ...
It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. ...
For such assistance I thank Wim Blok, Max Cresswell, John Dawson, Allen Emerson, Saul Kripke, Neil Leslie, Ed Mares, Robin Milner, Hiroakira Ono, Lawrence Pedersen, Vaughan Pratt, Colin Stirling and Paul ...
doi:10.1016/s1570-8683(03)00008-9
fatcat:zhwzfvdeqjg3rgbkqstbxk5yqq
Duality between unprovability and provability in forward proof-search for Intuitionistic Propositional Logic
[article]
2018
arXiv
pre-print
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To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability which is prone to constructively ascertain the unprovability of a formula G by providing a concise countermodel for it; ...
Here we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. ...
Finally, as a future work we plan to investigate the applicability of our method to other logics, in particular to modal logics such as S4 and intermediate logics such as Gödel-Dummett logic characterized ...
arXiv:1804.06689v1
fatcat:hjlq6rvi7zgild2imvnnyvzd7m
A New Unified Account of Truth and Paradox
2015
Mind
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In Gentzen's original systems, one can literally perform a cut, by applying the Cut Rule of the sequent calculus: D : l l, G : w D, G : w -or, in the case of natural deductions, by grafting a copy of one's ...
, Dummett 1991 , and Tennant 1997 Here, I shall be concerned only with the reduction procedures that will be needed for a discussion of certain standard paradoxes. ...
to undertake whatever rational revision of one's beliefs might be called for. 9 ...
doi:10.1093/mind/fzu179
fatcat:dlf6xksza5dpdhqlr3vnylljre
Fast Decision Procedure for Propositional Dummett Logic Based on a Multiple Premise Tableau Calculus
unpublished
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We present a procedure to decide propositional Dummett logic. Such a procedure relies on a tableau calculus with a multiple premise rule and optimizations. ...
For this reason another name for the logic under consideration is Gödel-Dummett Logic. ...
We quote [8] for a throughout treatment of the subject. In the late '90 were presented tableau [1, 11] and sequent calculi [10] for propositional Dummett logic. ...
doi:10.29007/mbbq
fatcat:le3w6wt3wje3hivj3cj32h7dmm
Proof theory and proof search of bi-intuitionistic and tense logic
[article]
2018
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Our calculus is sound, semantically complete and allows terminating backward proof search, hence giving rise to a decision procedure for bi-intuitionistic logic. ...
The interaction between these dual connectives makes it non-trivial to develop a cut-free sequent calculus for these logics. ...
logic called Gödel-Dummett logic. ...
doi:10.25911/5d5fcc3a4db33
fatcat:r5767wlm7jbozcdo6dr7smkx7q
Proof Search in Multi-Agent Dialogues for Modal Logic
2018
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These are not only used as reasoning procedures for intuitionistic and classical logic, but also for intermediate logics like the Gödel-Dummett logic. ...
Multi-Proponent Dialogues (Forking and Merging) Fermüller and Ciabattoni [51] propose multi-proponent dialogues to cope with intuitionistic and the intermediate Gödel-Dummett Logic. ...
When searching for proofs, a normalization of deductions in a calculus is desired. A new attempt to find a normalized calculus leads to dialogical logic, a game-theoretic reasoning technique. ...
doi:10.20378/irbo-52527
fatcat:nov4b3rthzep5iqzrysujqzqb4
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