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Uniform Rules and Dialogue Games for Fuzzy Logics [chapter]

Agata Ciabattoni, Christian G. Fermüller, George Metcalfe
2005 Lecture Notes in Computer Science  
We provide uniform and invertible logical rules in a framework of relational hypersequents for the three fundamental t-norm based fuzzy logics i.e., Łukasiewicz logic, Gödel logic, and Product logic.  ...  Such a framework can be interpreted via a particular class of dialogue games combined with bets, where the rules reflect possible moves in the game.  ...  We have presented invertible uniform logical rules for the fundamental t-norm based fuzzy logics Ł, G, and Π, that both provide the basis for Co-NP decision procedures, and may be interpreted within a  ... 
doi:10.1007/978-3-540-32275-7_33 fatcat:gikq37lo2zfj5madltav7da6uq

Randomized game semantics for semi-fuzzy quantifiers

C. G. Fermuller, C. Roschger
2013 Logic Journal of the IGPL  
In particular the adequateness of simple dialogue game rules for so-called proportionality quantifiers is shown.  ...  Building on a generalization of classical Henkin-Hintikka evaluation games to Giles' game semantics for Lukasiewicz logic, a concept for evaluating (semi-)fuzzy quantifiers by randomizing the choice of  ...  For the logical rules of his game Giles referred not to Henkin or Hintikka, but to Lorenzen's dialogue game semantics for intuitionistic logic [15] .  ... 
doi:10.1093/jigpal/jzt049 fatcat:fg5pg46w5fg67okaav2lx7xkxy

Randomized Game Semantics for Semi-fuzzy Quantifiers [chapter]

Christian G. Fermüller, Christoph Roschger
2012 Communications in Computer and Information Science  
In particular the adequateness of simple dialogue game rules for so-called proportionality quantifiers is shown.  ...  Building on a generalization of classical Henkin-Hintikka evaluation games to Giles' game semantics for Lukasiewicz logic, a concept for evaluating (semi-)fuzzy quantifiers by randomizing the choice of  ...  For the logical rules of his game Giles referred not to Henkin or Hintikka, but to Lorenzen's dialogue game semantics for intuitionistic logic [15] .  ... 
doi:10.1007/978-3-642-31724-8_66 fatcat:du5a72owtzbsjlqfdgdxx3mjs4

Combining Supervaluation and Degree Based Reasoning Under Vagueness [chapter]

Christian G. Fermüller, Robert Kosik
2006 Lecture Notes in Computer Science  
On the other hand, t-norm based fuzzy logics model truth functional reasoning, where reals in the unit interval [0, 1] are interpreted as degrees of truth.  ...  We show that both types of reasoning can be combined within a single logic SŁ, that extends both: Łukasiewicz logic Ł and (classical) S5, where the modality corresponds to '. . . is true in all complete  ...  Reasoning via dialogue games We have defined the logic SŁ in an attempt to relate supervaluation and 'fuzzy valuation' in a common framework based on precisification spaces.  ... 
doi:10.1007/11916277_15 fatcat:qprykkz2unfs5adgwr6edfps5a

From Games to Truth Functions: A Generalization of Giles's Game

Christian G. Fermüller, Christoph Roschger
2014 Studia Logica: An International Journal for Symbolic Logic  
Motivated by aspects of reasoning in theories of physics, Robin Giles defined a characterization of infinite valued Lukasiewicz logic in terms of a game that combines Lorenzen-style dialogue rules for  ...  We analyze this game and provide conditions on payoff functions that allow us to extract many-valued truth functions from dialogue rules of a quite general form.  ...  corresponds to a quite remarkable (hypersequent) calculus with uniform rules for all three fundamental t-norm based fuzzy logics.  ... 
doi:10.1007/s11225-014-9550-7 fatcat:awsiavg5e5hqhlvxbkpnwabsli

Hintikka-Style Semantic Games for Fuzzy Logics [chapter]

Christian G. Fermüller
2014 Lecture Notes in Computer Science  
Various types of semantics games for deductive fuzzy logics, most prominently for Lukasiewicz logic, have been proposed in the literature.  ...  logic' or even simply as 'fuzzy logic' [27] .  ...  and Majer [4] , and Giles's dialogue and betting game [12, 13] .  ... 
doi:10.1007/978-3-319-04939-7_9 fatcat:zad6cy6bmfe2bmqj6ksbarbrha

Hintikka Style Game Rules for Semi-Fuzzy Quantifiers

Christian G. Fermueller, Matthias F. J. Hofer
2017 2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)  
The simple format of Hintikka-style games is compared to the seemingly much more general one of Giles's game for Łukasiewicz logic.  ...  Extending Hintikka's game for the evaluation of classical formulas, we explore the realm of quantifier rules that can be defined by combining several moves consisting of choices by the two strategic players  ...  We thank Paoli Baldi and Christoph Roschger for valuable comments on an earlier version of this paper.  ... 
doi:10.1109/ismvl.2017.57 dblp:conf/ismvl/FermullerH17 fatcat:vrydx2r5azcovgyqiax5ql2erm

Giles's Game and the Proof Theory of Łukasiewicz Logic

Christian G. Fermüller, George Metcalfe
2009 Studia Logica: An International Journal for Symbolic Logic  
In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies  ...  for the game corresponds to the validity of formulas in Lukasiewicz logic.  ...  for intuitionistic logic and Lorenzen's original dialogue game.  ... 
doi:10.1007/s11225-009-9185-2 fatcat:aggj6lj3ebcq5l6tzkebbxjrtu

Page 6922 of Mathematical Reviews Vol. , Issue 93m [page]

1993 Mathematical Reviews  
ISBN 0-7923-1358-5 Contents: Didier Dubois and Henri Prade, The semantics of fuzzy “if ... then ...” rules (3-16); Vilém Novak, On the logical basis of approximate reasoning (17-27); Janusz Kacprzyk and  ...  , Algorithms for projecting points ito give the most uniform distribution with applications to hashing (572-590); Feng Gao [Feng Gao*], Leonidas J.  ... 

Dialogue Protocols for Formal Fallacies

Magdalena Kacprzak, Olena Yaskorska
2014 Argumentation: an international journal on reasoning  
The system is inspired by Hamblin's formal dialectic and Lorenzen's dialogical logic. It offers uniform protocols for Hamblin's and Lorenzen's dialogues and adds a protocol for embedding them.  ...  The LHND system is compared to Walton and Krabbe's Complex Persuasion Dialogue using an example of a dialogue.  ...  and the source are credited.  ... 
doi:10.1007/s10503-014-9324-4 fatcat:ue6jv7af65c3fbwinktgcpgome

Action and Procedure in Reasoning [chapter]

Johan van Benthem
2002 Studies in Fuzziness and Soft Computing  
Dialogue games have logical rules breaking down formulas much like those in our earlier games.  ...  For, in addition to the non- controversial logical rules regulating a dialogue, one must agree on what may be called procedural conventions.  ... 
doi:10.1007/978-3-7908-1792-8_12 fatcat:rrfuqz4cm5a5fe6gq3fxwl43aq

Trichotomic Argumentation Representation [article]

Merlin Göttlinger, Lutz Schröder
2018 arXiv   pre-print
With the recent extensions AIF+ and Social Argument Interchange Format (S-AIF), which embed dialogue and speakers into the AIF argumentation representation, the basis for representing all three aspects  ...  The Aristotelian trichotomy distinguishes three aspects of argumentation: Logos, Ethos, and Pathos.  ...  We use the standard Łukasiewicz semantics of fuzzy logic (see Lukasiewicz and Straccia [23] for an overview): Definition 4 (Łukasiewicz Semantics [23] ).  ... 
arXiv:1812.06745v1 fatcat:busug3z2uzcrlgn6nkz6dusvdu

Fuzzy sets and formal logics

Lluís Godo, Siegfried Gottwald
2015 Fuzzy sets and systems (Print)  
The paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics.  ...  Acknowledgments The authors are grateful to an anonymous reviewer and to Carles Noguera for their useful comments and suggestions.  ...  Godo acknowledges partial support by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and 2014 SGR 118.  ... 
doi:10.1016/j.fss.2015.06.021 fatcat:jstlgpnzrze3pkikat2rcbeeh4

Strategies for offer generation and relaxation in fuzzy constraint-based negotiation models

Miguel A. Lopez-Carmona, Ivan Marsa-Maestre, Juan R. Velasco, Enrique de la Hoz, Bernardo Alarcos, Minjie Zhang, Takayuki Ito
2010 Multiagent and Grid Systems  
It is recognized that fuzzy constraints represent an efficient way of capturing requirements and preferences, and an useful mechanism for representing trade-offs.  ...  Most approaches are mainly focused on using constraints as a framework for describing preferences, and few works focus on using them as an element in the communication process itself in order to elaborate  ...  Acknowledgements This work has been supported by the Spanish Ministry of Education and Science grant TIN2008-06739-C04-04.  ... 
doi:10.3233/mgs-2010-0163 fatcat:wkynvltqv5h5nmej3kelkxr2la

A Predict-Fuzzy Logic Communication Approach for Multi Robotic Cooperation and Competition

Tingkai Wang, Quan Dang, Peiyuan Pan
2011 Journal of Communications  
behavior and a fuzzy communication approach.  ...  Based on the intelligent communication strategy, two robots playing a zero-sum game of hide-and-seek and two cooperative robots competing against a third robot have been explored.  ...  PREDICT-FUZZY LOGIC COMMUNICATION The Predict-Fu zzy Logic Co mmun ication system contains a semantics and grammar for co mmunicating, robot performance rule base, fuzzy logic base, a fuzzy inference engine  ... 
doi:10.4304/jcm.6.3.225-231 fatcat:cocksgjtjvawxlba4vvwl7nxxq
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