Site UMMO-SCIENCES - TETRAVALENCE 1

TETRAVALENCE 1

Bibliographie concernant la tétravalence
(Pierre Orion)

Le sujet de la logique tétravalente mobilise de plus en plus dirait-on. On se souvient des premiers messages de Seth sur la logique tétravalente, et qui avaient suscité (comme d'autres messages) quelques commentaires. J'avais moi-même souhaité en savoir un peu plus. C'est chose faite. Une analyse bibliographique du sujet montre effectivement une abondande littérature scientifique, avec des connexions aux domaines cités par Seth. On trouvera une cinquantaine de références d'articles, avec les abstracts, en fin de mon message, classées par thèmes. J'ajoute un autre mail avec tous les autres références, non classées, pour ceux que ça intéresse. On retrouve les thèmes décrits par Seth (informatique théorique et appliquée, mathématiques et logique formelle, intelligence artificielle, électronique, ordinateurs quantiques, psychologie). Le résumé de chaque référence permet de se faire une idée du sujet abordé. Pour se procurer le texte complet, en général il faut passer commande auprès de l'éditeur. Certains articles sont quelquefois disponibles en pdf sur le web.
On comprend alors mieux les réactions de Seth, qui, à mon avis, ne sont pas celles d'un initié qui cherche à faire mystère, mais plutôt celles de quelqu'un qui découvre le sujet et cherche à le comprendre en profondeur.
Même pour un mathématicien érudit, ce travail prend des mois. Ensuite, faire progresser le sujet par confrontation avec les textes ummites peut prendre des années avant d'aboutir à quelque chose. Avant ce n'est pas sérieux. Rien à voir avec l'impatience affiché par certains et l'effervescence de la liste où les messages déboulent quotidiennement. C'est vrai qu'il existe un travail de répertoire, de classification des informations contenus dans les lettres ummites. Il est important pour la diffusion et la compréhension des informations et je ne le critique pas. Mais nous avons aussi besoin de faire de la recherche scientifique.

On se doute que l'approche terrienne de la logique tétravalente soit différente, sur le plan ontologique, de l'approche ummite. C'est là où c'est intéressant. Mais nous nous devons, pour l'étude de ce sujet, d'assimiler d'abord ce qui s'est déjà fait sur terre. Sinon, nous allons être vite limités et fonctionner en cercle fermé, et nous risquons de réinventer l'eau chaude.

 

Jacques Pazelle nous introduit au système de Belnap (référence : N.D. Belnap. A useful four-valued logic, pages 7-37. Modern Uses of MultipleValued Logic. Reidel, 1977.), qui sont des travaux parmi d'autres.

Comme introduction on peut consulter le passage du Stanford Encyclopedie sur les logiques multivaluées : http://plato.stanford.edu/archives/fall2002/entries/logic-manyvalued/

On y trouve entre autres une série de références d'ouvrages, ainsi qu'un bref aperçu historique.

Enfin j'attire l'attention sur cet article :
TI:  The solution of logical equations
AU:  Lobanov,-I.
SO:  Automatic-Documentation-and-Mathematical-Linguistics. 1998; 32(5): 16-27; Original: Nauchno-Tekhnicheskaya-Informatsiya,-Seriya-2. 1998; (9): 34-40
PB:  Allerton Press
AB:  The article considers the process of solving logical equations and proposes a simple method that makes it possible to solve logical equations with a large number of two-valued variables. Methods are developed for minimization of functions in three- and four-valued logics for two-valued arguments. A complete system of inverse functions is constructed by means of the proposed methods. It is proved that a rigorous result may be obtained only in four-valued logic.



Références bibliographiques sur la logique tétravalente, classées par thèmes.

- Sur les ordinateurs quantiques :

Quantum computer with mixed states and four-valued logic
Tarasov,-Vasily-E. (Skobeltsyn Institute of Nuclear Physics, Moscow State
University, Moscow (Russian Federation)). E-mail: tarasov@theory.sinp.msu.r
Journal-of-Physics.-A,-Mathematical-and-General (28 Jun 2002) v. 35(25) p. 5207-5235
Country of input: International Atomic Energy Agency (IAEA); DOI: 10.1088/0305-4470/35/25/305  Available online at the Web site for the Journal of Physics. A, Mathematical and General (ISSN 4361-6447) http://www.iop.org/
English
In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4 sup n -dimensional operator Hilbert space (Liouville space). It allows us to use a quantum computer model with four-valued logic. The gates of this model are general superoperators which act on n-ququat state. Ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n-qubit open system are considered as four-valued logic gates acting on n-ququats. We discuss properties of quantum four-valued logic gates. In the paper we study universality for quantum four-valued logic gates. (author) 33-035833 EBSCO Online
http://ejournals.ebsco.com/direct.asp?ArticleID=600H4KBR5KA355B65K44
InformationQuest http://www.eiq.com/usr_login.html?sici=0305-4470%28000000%2935%3A25%3C5207%3 AX%3E2.0.CO%3B2-X
Commander par : FORM@INIST
http://services.inist.fr/cgi-bin/manage?modele=fre/form01.htm&a=remplir&orig ine=B&numero_document=[SP_MACRO]sp.rvalue field="SP$ISSN"[/SP_MACRO]&volume=[SP_MACRO]sp.rvalue
field="SP$VOLUME"[/SP_MACRO]&numero_fascicule=[SP_MACRO]sp.rvalue
field="SP$ISSUE"[/SP_MACRO]&annee_publication=[SP_MACRO]sp.rvalue
field="PY"[/SP_MACRO]&premiere_page=[SP_MACRO]sp.rvalue
field="SP$PAGE1"[/SP_MACRO]&type_document=PERIODIQUE""


Some physical applications of nonstandard logical systems. Quantum mechanics and possibility theory. Four-valued logic with fuzzy truth values.
Nekotorye fizicheskie primeneniya nestandartnykh sistem logiki. Kvantovaya mekhanika i teoriya vozmozhnosti. 4-znachnaya logika s nechetkimi istinnostnymi znacheniyami. Bogdanova,-N.B.; Kostenko,-B.F.
Joint Inst. for Nuclear Research, Dubna (USSR). Lab. of Computing Techniques and Automation. 1989. 10 p.
Availability: INIS
JINR-R--5-89-403 (JINRR589403) Russian
A four-valued propositional calculus with two fuzzy truth values which allows to describe physical phenomena with taking into account the Heisenberg uncertainty relation is suggested. It is shown that this logic complies with axioms and inference rules of the classical two-vaued logic Cl sub 2 and is characterized by the equivalence classes algebra which is isomorphous to the algebra of Cl sub 2. The meaning of the main logical operations is discussed in detail. 12 refs.; 2 figs.; 2 tabs. 22-038902

Some physical applications of nonstandard logical systems. Quantum mechanics and possibility theory. Four-valued logic with accidental truth values.
Nekotorye fizicheskie primeneniya nestandartnykh sistem logiki. Kvantovaya mekhanika i teoriya vozmozhnosti. 4-znachnaya logika so sluchajnymi istinnostnymi znacheniyami. Bogdanova,-N.B.; Kostenko,-B.F.
Joint Inst. for Nuclear Research, Dubna (USSR). Lab. of Computing Techniques and Automation. 1989. 9 p. Availability: INIS
JINR-R--5-89-402 (JINRR589402) Russian
A four-valued propositional calculus with two accidental truth values which corresponds to the empirical level of description of physical phenomena with taking into account the Heisenberg uncertainty relation is suggested. Some results of the traditional theory of the quantum measurement are reformulated in a form of simple rules for successive measurements. Arguments are brought showing orthodox or Copenhagen interpretation of quantum mechanics which postulates the coexistence of two different levels pf physical phenomena description (quantum and classical) may be determined more accurately on the basis of imaginations of the physical information transmission process. 12 refs.; 3 tabs.


-   en psychologie

TI:  An inconsistency tolerant model for belief representation and belief revision
AU:  Chopra,-S.; Parikh,-R.
ED:  Dean,-T.
SO:
IJCAI-99.-Proceedings-of-the-Sixteenth-International-Joint-Conference-on-Artificial-Intelligence. 1999: 192-7 vol.1
PB:  Morgan Kaufmann Publishers, San Francisco, CA, USA
AB:  We propose a model for representing and revising belief structures, which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's four-valued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computationally tractable procedures for query answering and belief base revision are obtained.

TI:  Relevance sensitive belief structures
AU:  Chopra,-S.; Parikh,-R.
SO:  Annals-of-Mathematics-and-Artificial-Intelligence. 2000; 28(1-4):
259-85
PB:  Baltzer
AB:  We propose a new relevance sensitive model for representing and revising belief structures, which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's four-valued logic. Axioms analogous to the axioms of Alchourron, Gardenfors and Makinson (1985) [AGM axioms] hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computationally tractable procedures for query answering and belief base revision are obtained.
PY:  2000
FTXT:  SwetsWise
http://www.SwetsWise.com/link/access_db?issn=1012-2443&vol=28&iss=1-4&page=2 59&FT=1

TI:  A four-valued logic B(4) of E(9) for modeling human communication
AU:  Rine,-D.; Alnakari,-R.
SO:
Proceedings-30th-IEEE-International-Symposium-on-Multiple-Valued-Logic-ISMVL
-2000. 2000: 285-90
PB:  IEEE Comput. Soc, Los Alamitos, CA, USA
AB:  In this paper a four-valued logic on B(4) called Hyawic Form UniLogic is presented. Examples of this UniLogic are given which model problems in the area of human interaction, dialog and communication, i.e., human speech. The four values, or states, are isolated, conflicting, coexisting and unifying, forming a square lattice of B(4), Post Algebra of order 2 with 4 elements, inside a Post Algebra on E(9) of order 3 with 9=3/sup */3 elements. This logic has been used to represent human speech problems and their solutions in college classrooms. This logic is used in different universities, countries and languages including France, Algeria, Egypt and USA. It is used for policy analysis and planning, as well as for academic research in inter-communications analysis. Software packages using this logic are available from the developer Dr. Raiek Alnakari.
IB:  0769506925
PY:  2000


-   en électronique et circuits intégrés

T1:  Multiple-valued logic-in-memory VLSI architecture based on floating-gate-MOS  pass-transistor logic
PA:  HANYU-T; KAMEYAMA-M
SO:  IEICE-Transactions-on-Electronics. 1999; v E82-C (9) : 1662-1668
IS:  0916-8524
PY:  1999
LA:  English
AB:  A new logic-in-memory VLSI architecture based on multiple-valued floating-gate-MOS pass-transistor logic is proposed to solve the communication bottleneck between memory and logic modules. Multiple-valued stored data are represented by the threshold voltage of a floating-gate MOS transistor, so that a single floating-gate MOS transistor is effectively employed to merge multiple-valued threshold-literal and pass-switch functions.  As an application, a four-valued logic-in-memory VLSI for high-speed pattern recognition is also presented.  The proposed VLSI detects a stored reference word with the minimum Manhattan distance between a 16-bit input word and 16-bit stored reference words.  The effective chip area, the switching delay and the power dissipation of a new four-valued full adder, which is a key component of the proposed logic-in-memory VLSI, are reduced to about 33 percent, 67 percent and 24 percent, respectively, in comparison with those of the corresponding binary CMOS implementation under a 0.5-<mu>m flash EEPROM technology.

T1:  Compact multiple-valued multiplexers using negative differential resistance  devices
PA:  CHAN-H-L; MOHAN-S; MAZUMDER-P; HADDAD-G-I
SO:  IEEE-Journal-of-Solid-State-Circuits. 1996; 31 (8) : 1151-1156
IS:  0018-9200
PY:  1996
LA:  English
AB:  Quantum electronic devices with negative differential resistance (NDR) characteristics have been used to design compact multiplexers. These multiplexers may be used either as analog multiplexers where the signal on a single select line selects one out of four analog inputs, or as four-valued logic multiplexers where the select line and the input lines represent one of four quantized signal values and the output line corresponds to the selected input. Any four-valued logic function can be implemented using only four-valued multiplexers (also known as T-gates), and this T-gate uses just 13 devices (transistors) as compared to 44 devices in CMOS. The design of the T-gate was done using a combination of resonant tunneling diodes (RTD's) and heterojunction bipolar transistors (HBT's) with the folded I-V characteristic (NDR characteristic) of the RTD's providing the compact logic implementation and the HBT's providing the gain and isolation. The application of the same design principles to the design of T-gates using other NDR devices such as resonant tunneling hot electron transistors
(RHET's) and resonant tunneling bipolar transistors (RTBT's) is also demonstrated.

TI:  Multiple-valued logic
AU:  Butler,-J.-T.
SO:  IEEE-Potentials. April-May 1995; 14(2): 11-14
AB:  The ultimate usefulness of a number system depends on its implementation. Multiple-valued logic has been implemented in charge-coupled devices (CCD). In this technology, logic values are encoded as charge. For example, prototype four-valued logic devices have been implemented at the University of Twente (Enschede, Holland). Hitachi has implemented a 16-valued memory that stores the equivalent of 10/sup 6/ bits. CCD is more compact than any other VLSI technology. Although it is slower than CMOS (complementary metal oxide semiconductor), it is much faster than the disk and has the potential of replacing the disk. The use of multiple-valued logic in CCD increases its storage capacity significantly. Multiple-valued logic has also been implemented in current-mode CMOS.

TI:  A four-valued logic and switch-level differences
AU:  Mou-Hu
SO:Proceedings.-The-Twenty-Fourth-International-Symposium-on-Multiple-Valued-Lo gic-Cat.-No.94CH3406-6. 1994: 362-7
PB:  IEEE Comput. Soc. Press, Los Alamitos, CA, USA
AB:  In this paper, the application of a four-valued logic to the switch-level test generation is studied. A switch-level operator fault model is proposed. Switch-level U difference and Z difference of a function to a fault are defined. A method to derive switch-level differences is given. Finally, a new switch-level test generation algorithm for CMOS circuits is presented.
IB:  0818656506
PY:  1994

TI:  Four-valued logic system and its application to describing the specification and design verification of combinational circuits
AU:  Miura,-Y.; Li,-J.; Wang,-L.; Naito,-S.
SO:  Computer-Systems-Science-and-Engineering. Jan. 1994; 9(1): 38-45
AB:  This paper proposes a novel four-valued logic system and its application to describing specification and verifying design. By the logic system, we can describe the specification for incompletely specified circuits easily and verify design by four-valued simulation. The logic system consists of four basic events. The system includes two basic events in the traditional two-valued logic system. First we show the completeness of the logic system. Then we present a method for describing specification, which is given as the set of correspondence from input vector sets to output vector sets. We also present a design verification method on the four-valued logic. The verification method is realized using backward simulation by the four-value. It is shown that the four-valued backward simulation can decrease the time complexity for verification.
PY:  1994

TI:  Pacific Rim Fault Tolerant Computing (PRFTC) Conference
SO:  Computer-Systems-Science-and-Engineering. Jan. 1994; 9(1):
AB:  The following topics were dealt with: fault tolerant computing for safety critical applications in Japan; comparison-based fault diagnosis in multiprocessor systems; algorithm for availability evaluation of multidimensional voting; hyper-geometric distribution model for hardware debugging process; WSI network design and its evaluation using yields; four-valued logic system; self-checking systems hierarchy; fault tolerant clock synchronisation algorithm; hardware designs verification and validation via hardware Petri nets.
PY:  1994


-   en informatique théorique et appliquée

T1:  Hypothesis support for information integration in four-valued logics.
Theoretical computer science : exploring new frontiers of theoretical informatics : Sendai, 17-19 August 2000
PA:  LOYER-Y; SPYRATOS-N; STAMATE-D; VAN-LEEUWEN-Jan, ed; WATANABE-Osamu,
ed; HAGIYA-Masami, ed; MOSSES-Peter-D, ed; ITO-Takayasu, ed
SO:  Lecture-notes-in-computer-science. 2000; 1872 : 536-548
IS:  0302-9743
PY:  2000
LA:  English
AB:  We address the problem of integrating information coming from different sources. The information consists of facts that a central server collects and tries to combine using (a) a set of logical rules, i.e. a logic program, and (b) a hypothesis representing the server's own estimates. In such a setting incomplete information from a source or contradictory information from different sources necessitate the use of many-valued logics in which programs can be evaluated and hypotheses can be tested. To carry out such activities we propose a formal framework based on Belnap's four-valued logic. In this framework we work with the class of programs defined by Fitting and we develop a theory for information integration. We also establish an intuitively appealing connection between our hypothesis testing mechanism on the one hand, and the well-founded semantics and Kripke-Kleene semantics of Datalog programs with negation, on the other hand.

T1:  Computing and comparing semantics of programs in four-valued logics.
MFCS '99 : mathematical foundations of computer science : Szklarska Poreba, 6-10 September 1999
PA:  LOYER-Y; SPYRATOS-N; STAMATE-D; KUTYOWSKI-Miroslalw, ed; PACHOLSKI-Leszek, ed; WIERZBICKI-Tomasz, ed
SO:  Lecture-notes-in-computer-science. 1999; 1672 : 59-69
IS:  0302-9743
PY:  1999
LA:  English
AB:  The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the assumption that every such atom is false, while the Kripke-Kleene semantics corresponds to the assumption that every such atom is unknown. In this paper, we propose to unify and extend this assumption-based approach by introducing parameterized semantics for logic programs. The parameter holds the value that one assumes for all atoms whose logical values cannot be inferred from the rules. We work within Belnap's four-valued logic, and we consider the class of logic programs defined by Fitting. Following Fitting's approach, we define a simple operator that allows us to compute the parameterized semantics, and to compare and combine semantics obtained for different values of the parameter. The semantics proposed by Fitting corresponds to the value false. We also show that our approach captures and extends the usual semantics of conventional logic programs thereby unifying their computation.
AN:  990504904

T1:  Towards a logical semantics for pure Prolog. 6th European Symposium on Programming
PA:  BARBUTI-R; DE-FRANCESCO-N; MANCARELLA-P; SANTONE-A; NIELSON-Hanne-Riis, ed
SO:  Science-of-computer-programming. 1998; 32 (1-3) : 145-176
IS:  0167-6423
PY:  1998
LA:  English
AB:  The coincidence of the declarative and procedural interpretations of logic programs does not apply to Prolog programs, due to the depth-first left-to-right evaluation strategy of Prolog interpreters. We propose a semantics for Prolog programs based on a four-valued logic. The semantics is based on a new concept of completion analogous to Clark's and it enjoys the nice properties of the declarative semantics of logic programming: existence of the least Herbrand model, equivalence of the model-theoretic and operational semantics.

T1:  Combining explicit negation and negation by failure via Belnap's logic
PA:  RUET-P; FAGES-F
SO:  Theoretical-computer-science. 1997; 171 (1-2) : 61-75
IS:  0304-3975
PY:  1997
LA:  English
AB:  Copyright (c) 1996 Elsevier Science B.V. All rights reserved. This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two different forms of reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued logic, and an answer sets&rsquo; semantics that is shown to be equivalent to that of Gelfond and Lifschitz. The proofs rely on a translation into normal programs, and on a variant of Fitting's extension of logic programming to bilattices.

TI:  Hypothesis support for information integration in four-valued logics
AU:  Loyer,-Y.; Spyratos,-N.; Stamate,-D.
ED:  van-Leeuwen,-J.; Watanabe,-O.; Hagiya,-M.; Mosses,-P.-D.; Ito,-T.
SO:
Theoretical-Computer-Science.-Exploring-New-Frontiers-of-Theoretical-Informatics.-International-Conference-IFIP-TCS-2000.-Proceedings-Lecture-Notes-in-Computer-Science-Vol.1872. 2000: 536-48
PB:  Springer-Verlag, Berlin, Germany
AB:  We address the problem of integrating information coming from different sources. The information consists of facts that a central server collects and tries to combine using: 1) a set of logical rules, i.e. a logic program, and 2) a hypothesis representing the server's own estimates. In such a setting incomplete information from a source or contradictory information from different sources necessitate the use of many-valued logics in which programs can be evaluated and hypotheses can be tested. To carry out such activities we propose a formal framework based on Belnap's four-valued logic. In this framework we work with the class of programs defined by fitting and we develop a theory for information integration. We also establish an intuitively appealing connection between our hypothesis testing mechanism on the one hand, and the well-founded semantics and Kripke-Kleene semantics of Datalog programs with negation, on the other hand.

TI:  Computing and comparing semantics of programs in four-valued logics
AU:  Loyer,-Y.; Spyratos,-N.; Stamate,-D.
ED:  Kutylowski,-M.; Pacholski,-L.; Wierzbicki,-T.
SO:
Mathematical-Foundations-of-Computer-Science-1999.-24th-International-Symposium,-MFCS'99.-Proceedings-Lecture-Notes-in-Computer-Science-Vol.1672. 1999: 59-69
PB:  Springer-Verlag, Berlin, Germany
AB:  The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the assumption that every such atom is false, while the Kripke-Kleene semantics corresponds to the assumption that every such atom is unknown. In this paper, we propose to unify and extend this assumption-based approach by introducing parameterized semantics for logic programs. The parameter holds the value that one assumes for all atoms whose logical values cannot be inferred from the rules. We work within Belnap's four-valued logic, and we consider the class of logic programs defined by Fitting. Following Fitting's approach, we define a simple operator that allows us to compute the parameterized semantics, and to compare and combine semantics obtained for different values of the parameter. The semantics proposed by Fitting corresponds to the value false. We also show that our approach captures and extends the usual semantics of conventional logic programs thereby unifying their computation.
IB:  3540664084
PY:  1999

TI:  DOLORES: a system for logic-based retrieval of multimedia objects
AU:  Fuhr,-N.; Govert,-N.; Rolleke,-T.
ED:  Bruce-Croft,-W.; Moffat,-A.; van-Rijsbergen,-C.-J.; Wilkinson,-R.;
Zobel,-J.
SO: Proceedings-of-the-21st-Annual-International-ACM-SIGIR-Conference-on-Research-and-Development-in-Information-Retrieval. 1998: 257-65
PB:  ACM, New York, NY, USA
AB:  We describe the design and implementation of a system for logic-based multimedia retrieval. As high-level logic for retrieval of hypermedia documents, we have developed a probabilistic object-oriented logic (POOL) which supports aggregated objects, different kinds of propositions (terms, classifications and attributes) and even rules as being contained in objects. Based on a probabilistic four-valued logic, POOL uses an implicit open world assumption, allows for closed world assumptions and is able to deal with inconsistent knowledge. POOL programs and queries are translated into probabilistic Datalog programs which can be interpreted by the HySpirit inference engine. For storing the multimedia data, we have developed a new basic IR system which yields physical data abstraction. The overall architecture and the flexibility of each layer supports logic-based methods for multimedia information retrieval.
IB:  1581130155
PY:  1998

TI:  Retrieval of complex objects using a four-valued logic
AU:  Rolleke,-T.; Fuhr,-N.
SO:  SIGIR-Forum. 1996; : 206-14
PB:  ACM
AB:  The aggregated structure of documents plays a key role in full text, multimedia, and network information retrieval (IR). Considering aggregation provides new querying facilities and improves retrieval effectiveness. We present a knowledge representation for IR purposes which pays special attention to this aggregated structure of objects. In addition, further features of objects can be described. Thus, the structure of full text documents, the heterogeneity and the spatial and temporal relationships of objects typical for multimedia IR, and meta information for network IR are representable within one integrated framework. The model we propose allows for querying on the content of documents (objects) as well as on other features. The query result may contain objects having different types. Instead of retrieving only whole documents, the retrieval process determines the least aggregated entities that imply the query.
PY:  1996


- en mathématiques et logique

T1:  Logical inference of clauses based on Petri net models
PA:  CHUANG-LIN; CHANSON-S-T
SO:  International-journal-of-intelligent-systems. 1998; 13 (9) : 821-840
IS:  0884-8173
PY:  1998
LA:  English
AB:  This paper extends the logical inference of Horn clauses in Petri net models to cover a large class of non-Horn clauses. Based on four-valued logic and the conflict transition concept, we show how the Petri net model for this class of non-Horn clauses can be constructed. The clause inference is solved by the T-invariant method or the fixpoint of markings. Both forward and backward inference can be used in our model. It is further shown that these techniques are efficient for the common classes of monotonic reasoning.
AN:  980440135
FTXT:  EBSCO Online
http://ejournals.ebsco.com/direct.asp?ArticleID=BV9BMNFA9EJRKNC19RK6

T1:  Motivation and demotivation of a four-valued logic
PA:  FOX-J
SO:  Notre-Dame-Journal-of-formal-Logic. 1990; 31 (1) : 76-80
IS:  0029-4527
PY:  1990
LA:  English
AB:  Belnap offers two arguments for the usefulness of four-valued logic. I argue that one of them, which rests on interpreting valuations as states of our information, when taken seriously collapses into an argument for two-valued logic in which relevance is lost, and that the other, resting on Scott's thesis, is not an argument for its usefulness

TI:  A first order, four-valued, weakly paraconsistent logic and its relation with rough sets semantics
AU:  Tsoukias,-A.
SO:  Foundations-of-Computing-and-Decision-Sciences. 2002; 27(2): 77-96
PB:  Inst. Comput. Sci. Poznan Univ. Technol. Poland
AB:  A first order four-valued logic, called DDT, is presented in the paper as an extension of Belnap's logic using a weak negation and establishing an appropriate semantic for the predicate calculus. The logic uses a simple algebraic structure, that is the smallest non trivial interlaced bilattice on the four truth values, thus resulting in a boolean algebra on the set of truth values. The logic is a language for reasoning under uncertainty, enabling to capture hesitation due either to inconsistent or incomplete information, while keeping a clear distinction between these epistemic states. The logic was originally developed for preference modelling purposes (for which a brief account is given in the paper). The paper demonstrates and discusses the equivalence between the semantics of this logic and of rough sets semantics. On this basis, this papers presents the possibility of inducing rules from examples, that can be integrated in systems whose inference is expressed in the above logic. Such an approach enhances the potentialities of the use of rough sets in classification, reasoning and decision support.

TI:  Relative sets and rough sets
AU:  Mousavi,-A.; Jabedar-Maralani,-P.
SO:  International-Journal-of-Applied-Mathematics-and-Computer-Science. 2001; 11(3): 637-53
PB:  Tech. Univ. Zielona Gora; Lubusky Sci. Soc. Zielona Gora
AB:  In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.

TI:  Relative completeness with respect to two unary functions
AU:  Pantovic,-J.; Tosic,-R.; Vojvodic,-G.
SO:  Discrete-Applied-Mathematics. 15 Oct. 2001; 113(2-3): 337-42
PB:  Elsevier
AB:  One of the most important results is the fact that the number of clones
is a continuum for k>or=3, while the corresponding set for k=2 is countable.
This shows a sharp difference when we go from the binary to the ternary
case. This paper discusses the relative completeness with respect to the
clone generated by two unary functions and show the sharp difference when we
go from four-valued logic to k-valued logic for k>4, as well. The number of
maximal clones over a finite set is finite and increases when k increases.
However, there are two relative maximal clones if k=3, 4 and there is one
relative maximal clone if k>4.

TI:  The solution of logical equations
AU:  Lobanov,-I.
SO:  Automatic-Documentation-and-Mathematical-Linguistics. 1998; 32(5): 16-27; Original: Nauchno-Tekhnicheskaya-Informatsiya,-Seriya-2. 1998; (9): 34-40
PB:  Allerton Press
AB:  The article considers the process of solving logical equations and proposes a simple method that makes it possible to solve logical equations with a large number of two-valued variables. Methods are developed for minimization of functions in three- and four-valued logics for two-valued arguments. A complete system of inverse functions is constructed by means of the proposed methods. It is proved that a rigorous result may be obtained only in four-valued logic.

TI:  Displaying the modal logic of consistency
AU:  Wansing,-H.
SO:  Journal-of-Symbolic-Logic. Dec. 1999; 64(4): 1573-90
PB:  Assoc. Symbolic Logic
AB:  It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.
PY:  1999

TI:  Comparison of logic operators for use in multiple-valued sum-of-products expressions
AU:  Hozumi,-T.; Kakusho,-O.; Hata,-Y.
SO:  IEICE-Transactions-on-Information-and-Systems. May 1999; E82-D(5): 933-9
PB:  Inst. Electron. Inf. & Commun. Eng
AB:  This paper shows the best operators for sum-of-products expressions. We first describe conditions of functions for product and sum operations. We examine all two-variable functions and select those that meet the conditions and then evaluate the number of product terms needed in the minimum sum-of-products expressions when each combination of selected product and sum functions is used. As a result of this, we obtain three product functions and nine sum functions in three-valued logic. We show that each of three product functions can express the same functions and MODSUM function is the most suitable for reduction of product terms. Moreover, we show that similar results are obtained in four-valued logic.
PY:  1999

TI:  A four-valued fuzzy propositional logic
AU:  Straccia,-U.
ED:  Pollack,-M.-E.
SO:
IJCAI-97.-Proceedings-of-the-Fifteenth-International-Joint-Conference-on-Artificial-Intelligence. 1997: 128-33 vol.1
PB:  Morgan Kaufmann Publishers, San Francisco, CA, USA
AB:  It is generally accepted that knowledge based systems would be smarter and more robust if they can manage inconsistent, incomplete or imprecise knowledge. This paper is about a four-valued fuzzy propositional logic, which is the result of the combination of a four-valued logic and a fuzzy propositional logic. Besides the nice computational properties, the logic enables us also to deal both with inconsistency and imprecise predicates in a simple way.
IB:  1558604804
PY:  1997

TI:  Reed-Muller-Fourier versus Galois field representations of four-valued logic functions
AU:  Stankovic,-R.-S.; Jankovic,-D.; Moraga,-C.
SO: Proceedings.-1998-28th-IEEE-International-Symposium-on-Multiple-Valued-Logic -Cat.-No.98CB36138. 1998: 186-91
PB:  IEEE Comput. Soc, Los Alamitos, CA, USA
AB:  In this paper, we introduce Reed-Muller-Fourier representations of four-valued functions over the ring of integers modulo 4 and compare them with the Galois field representations over GF(4). It is reported that on the average Reed-Muller-Fourier representations exhibit a lower complexity than those based on Galois field polynomials.
IB:  0818683716
PY:  1998

TI:  A proof method for the six-valued logic for incomplete information
AU:  Akama,-S.
SO:
Proceedings.-1997-27th-International-Symposium-on-Multiple-Valued-Logic-Cat. -No.97CB36061. 1997: 223-6
PB:  IEEE Comput. Soc. Press, Los Alamitos, CA, USA
AB:  O. Garcia and M. Moussavi (1990) proposed a six-valued logic to model incomplete information. Although their logic is promising, it lacks a proof theory to serve as a basis for automated reasoning. We describe a sequent style proof method for the logic and show that the consequence relation in the logic is equivalent to the one by N.D. Belnap's (1977) four-valued logic. We also suggest alternative formal interpretations for the logic.
IB:  0818679107
PY:  1997

TI:  Combining explicit negation and negation by failure via Belnap's logic
AU:  Ruet,-P.; Fages,-F.
SO:  Theoretical-Computer-Science. 15 Jan. 1997; 171(1-2): 61-75
PB:  Elsevier
AB:  This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two different forms of reasoning in the presence of incomplete information. Such programs have been introduced by M. Gelfond and V. Lifschitz (1988) and called extended programs. We provide them with a logical semantics in the style of K. Kunen (1987), based on Belnap's four-valued logic, and an answer set's semantics that is shown to be equivalent to that of Gelfond and Lifschitz. The proofs rely on a translation into normal programs, and on a variant of M. Fitting's extension of logic programming to bilattices.
PY:  1997
FTXT:  ScienceDirect (tm)
http://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SilverLinker&_ur
lversion=4&_method=citationSearch&_volkey=0304%2d3975%23171%2361&_version=1&
md5=e3d0de65b957cabbc9398cc10841e93f SwetsWise

TI:  Kleene's three valued logics and their children
AU:  Fitting,-M.
SO:  Fundamenta-Informaticae. March-May 1994; 20(1-3): 113-31
AB:  Kleene's strong three-valued logic extends naturally to a four-valued logic proposed by Belnap (1977). The author introduces a guard connective into Belnap's logic and considers a few of its properties. Then he shows that by using it four-valued analogs of Kleene's weak three-valued logic, and the asymmetric logic of Lisp are also available. He proposes an extension of these ideas to the family of distributive bilattices. Finally he shows that for bilinear bilattices the extensions do not produce any new equivalences.
PY:  1994


- sur les applications en intelligence artificielle

T1:  Bilattices and reasoning in artificial intelligence: Concepts and foundations
PA:  SIM-K-M
SO:  Artificial-Intelligence-Review. 2001; 15 (3) : 219-240
IS:  0269-2821
PY:  2001
LA:  English
AB:  The past few decades have seen a resurgence of reasoning techniques  in artificial intelligence involving both classical and non-classical logics. In his paper, "Multi-valued Logics: A Uniform Approach to Reasoning in Artificial Intelligence", Ginsberg has shown that through the use of bilattices, several reasoning techniques can be unified under a single framework. A bilattice is a structure that can be viewed as a class of truth values that can accommodate incomplete and inconsistent information and in certain cases default information. In bilattice theory, knowledge is ordered along two dimensions: truth/falsity and certainty/uncertainty. By defining the corresponding bilattices as truth spaces. Ginsberg has shown that the same theorem prover can be used to simulate reasoning in first order logic, default logic, prioritized default logic and assumption truth maintenance system. Although this is a significant contribution, Ginsberg's paper was lengthy and involved. This paper summarizes some of the essential concepts and foundations of bilattice theory. Furthermore, it discusses the connections of bilattice theory and several other existing multi-valued logics such as the various three-valued logics and Belnap's four-valued logic. It is noted that the set of four truth values in Belnap's logic form a lattice structure that is isomorphic to the simplest bilattice. Subsequently, Fitting proposed a conflation operation that can be used to select subsets of truth values from this and other bilattices. This method of selecting sub-sets of truth values provides a means for identifying sub-logic in a bilattice.
AN:  010231398
FTXT:  Kluwer Academic Publishers http://kapis.www.wkap.nl/oasis.htm/239899
EBSCO Online
http://ejournals.ebsco.com/direct.asp?ArticleID=XGJY5TLDDW1UMLGU92W3 Kluwer Journals@Ovid
http://gateway.ovid.com/ovidweb.cgi?T=JS&PAGE=fulltext&D=kap&NEWS=n&DBC=n&AN =239

TI:  FSimGEO: a test generation method for path delay fault test using fault simulation and genetic optimization
AU:  Sun-Yihe; Wu-Qifa
ED:  Mukund,P.-R.; Chickanosky,J.; Krishnamurthy,R.-K.
SO:
Proceedings-14th-Annual-IEEE-International-ASIC/SOC-Conference-IEEE-Cat.-No. 01TH8558. 2001: 225-9
PB:  IEEE, Piscataway, NJ, USA
AB:  Presents FSimGEO, an efficient test generation method for path delay fault test using fault simulation and genetic optimization. A parallel-vector fault simulator is introduced first, which can simulate several test vector pairs at the same time through introducing a four-valued logic and the path status graph (PSG) of the circuit structure. After this, a special genetic optimization algorithm is used to direct the process of searching and to optimize test sets generated. We have given the fitness function and genetic operators that affect the optimizing efficiency of genetic algorithm (GA) in detail. Experimental results have shown that the number of paths tested by FSimGEO is about 3.5 times that by other methods.


- Divers

TI:  Nearness relations in environmental space
AU:  Worboys,-M.-F.
SO:  International-Journal-of-Geographical-Information-Science. Oct.-Nov. 2001; 15(7): 633-51
PB:  Taylor & Francis
AB:  The notion of proximity is a fundamental component of any comprehensive ontology of space. This paper presents an experiment with human subjects concerning the vague spatial relation `near' in environmental space. After the topic is introduced and relevant previous work surveyed, the experiment is described. Three approaches to experimental analysis are presented and discussed: nearness neighbourhoods as regions with broad boundaries, fuzzy nearness and distance measures, and four-valued logic. Issues discussed in further detail are the truth gap-truth glut hypotheses regarding the psychology of vague predicates, and formal properties of the three-valued nearness relation. The conclusion is drawn that formal theories can usefully underpin and be applied to reasoning with vague spatial notions, such as nearness.

 

Toute contribution à cette étude reste bienvenue : ajh@wanadoo.fr

Accueil > Activités > Sciences > Tétravalence > tétravalence 1