1,721,015 research outputs found
Is multiset consequence trivial?
No full textDave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in (affine) linear logic does not motivate cut
Handbook of Mathematical Fuzzy Logic. Volume 1
Full text linkOriginating as an attempt to provide solid logical foundations
for fuzzy set theory, and motivated also by philosophical
and computational problems of vagueness and imprecision,
Mathematical Fuzzy Logic (MFL) has become a significant
subfield of mathematical logic. Research in this area focuses
on many-valued logics with linearly ordered truth values and
has yielded elegant and deep mathematical theories and
challenging problems, thus continuing to attract an ever
increasing number of researchers.
This two-volume handbook provides an up-to-date systematic
presentation of the best-developed areas of MFL. Its intended
audience is researchers working on MFL or related fields, who
may use the text as a reference book, and anyone looking for
a comprehensive introduction to MFL. Despite being located
in the realm of pure mathematical logic, this handbook will
also be useful for readers interested in logical foundations of
fuzzy set theory or in a mathematical apparatus suitable for
dealing with some philosophical and linguistic issues related
to vagueness.
The first volume contains a gentle introduction to MFL, a
presentation of an abstract algebraic framework for MFL,
chapters on proof theory and algebraic semantics of fuzzy
logics, and, finally, an algebraic study of Hájek’s logic BL.
The second volume is devoted to Łukasiewicz logic and MValgebras,
Gödel-Dummett logic and its variants, fuzzy logics
in expanded propositional languages, studies of functional
representations for fuzzy logics and their free algebras,
computational complexity of propositional logics, and
arithmetical complexity of first-order logics
Handbook of Mathematical Fuzzy Logic. Volume 3
No full textOriginating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This handbook provides, through its several volumes, an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. This handbook will be useful not only for readers interested in pure mathematical logic, but also for those interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. This third volume starts with three chapters on semantics of fuzzy logics, namely, on the structure of linearly ordered algebras, on semantic games, and on Ulam-Rényi games; it continues with an introduction to fuzzy logics with evaluated syntax, a survey of fuzzy description logics, and a study of probability on MV-algebras; and it ends with a philosophical chapter on the role of fuzzy logics in theories of vagueness
Slabě implikační predikátové fuzzy logiky
No full textThere are two classes of propositional logics related to the area of mathematical fuzzy logics proposed in work of the author (see also joint paper by the author and Libor Běhounek where philosophical, methodological, and pragmatical reasons for introducing these two classes appear.) After we recall same basic definitions we turn our attention to the first-order variants of these two classes of logics. The results presented here are mainly from the author's thesis and his upcoming paper. Because of the lack of space we present the basic definitions and theorems only and we completely disregard the important concept of Baaz delta
These degrees go to eleven: fuzzy logics and gradable predicates
No full textIn the literature on vagueness one finds two very different kinds of degree theory. The dominant kind of account of gradable adjectives in formal semantics and linguistics is built on an underlying framework involving bivalence and classical logic: its degrees are not degrees of truth. On the other hand, fuzzy logic based theories of vagueness—largely absent from the formal semantics literature but playing a significant role in both the philosophical literature on vagueness and in the contemporary logic literature—are logically nonclassical and give a central role to the idea of degrees of truth. Each kind of degree theory has a strength: the classical kind allows for rich and subtle analyses of the comparative form of gradable adjectives and of various types of gradable precise adjectives, while the fuzzy kind yields a compelling solution to the sorites paradox. This paper argues that the fuzzy kind of theory can match the benefits of the classical kind and hence that the burden is on the latter to match the advantages of the former. In particular, we develop a new version of the fuzzy logic approach that—unlike existing fuzzy theories—yields a compelling analysis of the comparative as well as an adequate account of gradable precise predicates, while still retaining the advantage of genuinely solving the sorites paradox
Algebraic semantics for one-variable lattice-valued logics
Full text linkThe one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic semantics for these logics have been obtained: most notably, for the modal counterparts S5 and MIPC of the one-variable fragments of first-order classical logic and intuitionistic logic, respectively. Outside the setting of first-order intermediate logics, however, a general approach is lacking. This paper provides the basis for such an approach in the setting of first-order lattice-valued logics, where formulas are interpreted in algebraic structures with a lattice reduct. In particular, axiomatizations are obtained for modal counterparts of one-variable fragments of a broad family of these logics by generalizing a functional representation theorem of Bezhanishvili and Harding for monadic Heyting algebras. An alternative proof-theoretic proof is also provided for one-variable fragments of first-order substructural logics that have a cut-free sequent calculus and admit a certain bounded interpolation property
Structural Completeness in Fuzzy Logics
No full textStructural completeness properties are investigated for a range of popular t-norm based fuzzy logics – including Lukasiewicz Logic, Gödel Logic, Product Logic, and Hájek’s Basic Logic – and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems
Admissible rules in the implication-negation fragment of intuitionistic logic
No full textAbstractUniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic IPC and its consistent axiomatic extensions (intermediate logics). A Kripke semantics characterization is given for the (hereditarily) structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of IPC form a PSPACE-complete set and have no finite basis
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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