Representations of monadic <Emphasis Type="Italic">MV</Emphasis> -algebras

Representations of monadic MV -algebra, the characterization of locally finite monadic MV -algebras, with axiomatization of them, definability of non-trivial monadic operators on finitely generated free MV -algebras are given. Moreover, it is shown that finitely generated m-relatively complete subalgebra of finitely generated free MV -algebra is projective.     

Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo's Logic MTL∀

The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono's Kripke semantics for the predicate version of FL_ew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order.     

Many-Valued Logics and Suszko's Thesis Revisited

Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were generated by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it.     

Axiomatic Extensions of IMT3 Logic

In this paper we characterize, classify and axiomatize all axiomatic extensions of the IMT3 logic. This logic is the axiomatic extension of the involutive monoidal t-norm logic given by ¬φ³ ∨ φ. For our purpose we study the lattice of all subvarieties of the class IMT3, which is the variety of IMTL-algebras given by the equation ¬(x³) ∨ x ≈ ?, and it is the algebraic counterpart of IMT3 logic. Since every subvariety of IMT3 is generated by their totally ordered members, we study the structure of all IMT3-chains in order to determine the lattice of all subvarieties of IMT3. Given a family of IMT3-chains the number of elements of the largest odd finite subalgebra in the family and the number of elements of the largest even finite subalgebra in the family turns out to be a complete classifier of the variety generated. We obtain a canonical set of generators and a finite equational axiomatization for each subvariety and, for each corresponding logic, a finite set of characteristic matrices and a finite set of axioms.     

A Common Abstraction of MV-Algebras and Abelian l-groups

We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.     

Semisimplicity,EDPC and Discriminator Varieties of Residuated Lattices

We prove that all semisimple varieties of FL _ew-algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FL _ew-algebras follows. It matches exactly a natural classification of logics over FL _ew proposed by H. Ono.     

Logit models and logistic regressions for social networks: III. Valued relations

This paper generalizes thep* model for dichotomous social network data (Wasserman & Pattison, 1996) to the polytomous case. The generalization is achieved by transforming valued social networks into three-way binary arrays. This data transformation requires a modification of the Hammersley-Clifford theorem that underpins thep* class of models. We demonstrate that, provided that certain (non-observed) data patterns are excluded from consideration, a suitable version of the theorem can be developed. We also show that the approach amounts to a model for multiple logits derived from a pseudo-likelihood function. Estimation within this model is analogous to the separate fitting of multinomial baseline logits, except that the Hammersley-Clifford theorem requires the equating of certain parameters across logits. The paper describes how to convert a valued network into a data array suitable for fitting the model and provides some illustrative empirical examples.This research was supported by grants from the Australian Research Council, the National Science Foundation (#SBR96-30754), and the National Institute of Health (#PHS-1RO1-39829-01).     

On relative universality and Q-universality

Adams and Dziobiak proved that any finite-to-finite universal quasivariety must be Q-universal, and then asked whether a somewhat weaker hypothesis could lead to the same conclusion. We show that their original hypothesis cannot be weakened to its naturally extreme form.To Professor Ale Pultr on his 65th birthdayThe authors gratefully acknowledge the support of the NSERC of Canada, of the project LN00A056 of the Czech Ministry of Education, and also of the Grant Agency of Czech Republic under the grant 201/02/0148.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

Volenti goes to Market*

If free markets consist in nothing more than “capitalist acts between consenting adults,” and if in the old legal maxim “volenti non fit injuria,” then it seems to follow that free markets do no wrongs. But that defense of free markets wrenches the “volenti” maxim out of context. In common law adjudication of disputes between two parties, it is perfectly appropriate to cast standards of “volenti” narrowly, and largely ignore “duress via third parties” (wrongs done to or by others who are not themselves party to the action). In economic markets, of course, those third-party effects are rife. But we want them to be rectified systematically, not piecemeal through particular cases between particular parties that happen to come to court. That is the proper province of political philosophers and system-designers, in critiquing and constraining the operation of the market. * I thank Peter Cane for much good advice, and exonerate him from any blame for the use I have made of it.     

Taking Degrees of Truth Seriously

This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the particular cases of Łukasiewicz’s many-valued logics and of logics associated with varieties of residuated lattices are also presented. Finally the extension of this paradigm to other, more general situations is discussed, highlighting the need for philosophical or applied motivations in the selection of the truth degrees, due both to the interpretation of the idea of truth degree and to some mathematical difficulties.     

Constructive Logic with Strong Negation is a Substructural Logic. I

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL _ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL _ew . Presented by Heinrich Wansing     

Network models for social influence processes

This paper generalizes thep* class of models for social network data to predict individual-level attributes from network ties. Thep* model for social networks permits the modeling of social relationships in terms of particular local relational or network configurations. In this paper we present methods for modeling attribute measures in terms of network ties, and so constructp* models for the patterns of social influence within a network. Attribute variables are included in a directed dependence graph and the Hammersley-Clifford theorem is employed to derive probability models whose parameters can be estimated using maximum pseudo-likelihood. The models are compared to existing network effects models. They can be interpreted in terms of public or private social influence phenomena within groups. The models are illustrated by an empirical example involving a training course, with trainees' reactions to aspects of the course found to relate to those of their network partners.This research was supported by grants from the Australian Research Council. The authors would like to acknowledge the help of Stanley Wasserman, Janice Langan-Fox and Larry Hubert, and would like to thank four anonymous reviewers for their helpful comments. Earlier versions of this article were presented at the North American Conference of the Psychometric Society, Lawrence, Kansas, June, 1999, and at the Australasian Mathematical Psychology Conference, Brisbane, Australia, December 1999.     

The Method of Socratic Proofs for Modal Propositional Logics: K5, S4.2, S4.3, S4F,S4R,S4M and G

The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5. Presented by Jacek Malinowski     

Electrical conductivity of Nd and Ce co-doped Gd2Zr2O7 ceramics

In this study, (Gd_{1? x} Nd _x )₂(Zr_{1? x} Ce _x )₂O₇ (0 ≤ x ≤ 0.5) ceramics have been prepared by pressureless sintering at 1973 K to investigate the influence of Nd and Ce co-doping on their electrical conductivity. The electrical conductivity of the ceramics was investigated by impedance spectroscopy measurements from 723 to 1173 K over the frequency range of 20 Hz to 2 MHz in air. The measured values obey the Arrhenius relation. For each composition, the grain conductivity gradually increases with increasing temperature from 723 to 1173 K. At a given temperature, it gradually decreases with increasing neodymium and cerium contents from x = 0 to 0.3; thereafter, the grain conductivity exhibits a slight increase with further increasing neodymium and cerium contents up to x = 0.5.