Sum of observables in fuzzy quantum spaces
We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.
Summable Family in a Commutative Group
Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6]. First, we compare the notions of the limit of a family indexed by a directed set, or a sequence, in a metric space [30], a real normed linear space [29] and a linear topological space [14] with the concept of the limit of an image filter [16]. Then, following Bourbaki [9], [10] (TG.III, §5.1 Familles sommables...
Sur la réfutabilité
Sur la théorie élémentaire des groupes libres
Sela a annoncé une solution complète d’un problème de Tarski, qui demanda vers 1945 quels sont les groupes de type fini qui ont la même théorie élémentaire qu’un groupe libre. Nous discuterons des travaux de Remeslennikov, Kharlampovich-Myasnikov, Sela, Champetier-Guirardel et autres sur la structure des groupes limites (les groupes de type fini qui sont “limites”de groupes libres, ou encore, qui ont la même théorie universelle qu’un groupe libre). Nous indiquerons quelques outils utilisés par Sela...
Sur le premier système de Lukasiewicz
Sur les algèbres de Heyting symétriques
Sur les éléments de construction de la logique mathématique
Il s'agit de présenter l'article de Schönfinkel «Über die Bausteine der mathematischen Logik», préparé pour la publication (1924) par H. Behmann, d'après une conférence de Schönfinkel en 1920, qui fonde ce que Curry nommera «la logique combinatoire». L'objectif principal du travail de Schönfinkel est l'élimination générale des variables (propositionnelles, prédicatives, individuelles), grâce à l'usage de plusieurs «fonctions particulières». On trouvera ici : (1) une introduction à l'article de Schönfinkel,...
Sur les systèmes déductifs dans la logique -valente
Sur quelques théorèmes fondamentaux de l'algèbre moderne
Symmetric implicational restriction method of fuzzy inference
The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy...
Syntaktické metody matematické logiky
Synthetic compontents of infinite classes of postulates.
(T, ⊥, N) fuzzy logic.
To investigate more reasonable fuzzy reasoning model in expert systems as well as more effective logical circuit in fuzzy control, a (T, ⊥, N) fuzzy logic is proposed in this paper by using T-norm, ⊥-norm and pseudo-complement N as the logical connectives. Two aspects are discussed: (1) some concepts of (T, ⊥, N) fuzzy logic are introduced and some properties of (T, ⊥, N) fuzzy logical formulae are discussed. (2) G-fuzzy truth (falsity) of (T, ⊥, N) fuzzy logical formulae are investigated and also...
Tableaux de Smullyan, ensembles de Hintikka et tout ça : un point de vue algébrique
On se propose de donner une interprétation algébrique (en calcul des propositions classiques) des notions d'arbres, d'ensembles de Hintikka, de la méthode des tableaux de Beth-Hintikka Smullyan.
Taclets: a new paradigm for constructing interactive theorem provers.
Frameworks for interactive theorem proving give the user explicit control over the construction of proofs based on meta languages that contain dedicated control structures for describing proof construction. Such languages are not easy to master and thus contribute to the already long list of skills required by prospective users of interactive theorem provers. Most users, however, only need a convenient formalism that allows to introduce new rules with minimal overhead. On the the other hand, rules...
Tarski Geometry Axioms – Part II
In our earlier article [12], the first part of axioms of geometry proposed by Alfred Tarski [14] was formally introduced by means of Mizar proof assistant [9]. We defined a structure TarskiPlane with the following predicates: of betweenness between (a ternary relation), of congruence of segments equiv (quarternary relation), which satisfy the following properties: congruence symmetry (A1), congruence equivalence relation (A2), congruence identity (A3), segment construction (A4), SAS (A5), betweenness...
Tarski's problem about the elementary theory of free groups has a positive solution.
Tavole semantiche per sistemi astratti di logica estensionale
Temi geometrici e di teoria della dimostrazione nelle logiche proposizionali di Łukasiewicz
The algebra of first-order fuzzy logic