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
The alternation hierarchy for the theory of -lattices.
The Axiomatization of Propositional Linear Time Temporal Logic
The article introduces propositional linear time temporal logic as a formal system. Axioms and rules of derivation are defined. Soundness Theorem and Deduction Theorem are proved [9].
The Axiomatization of Propositional Logic
This article introduces propositional logic as a formal system ([14], [10], [11]). The formulae of the language are as follows φ ::= ⊥ | p | φ → φ. Other connectives are introduced as abbrevations. The notions of model and satisfaction in model are defined. The axioms are all the formulae of the following schemes α ⇒ (β ⇒ α), (α ⇒ (β ⇒ γ)) ⇒ ((α ⇒ β) ⇒ (α ⇒ γ)), (¬β ⇒ ¬α) ⇒ ((¬β ⇒ α) ⇒ β). Modus ponens is the only derivation rule. The soundness theorem and the strong completeness theorem are proved....
The Basic Existence Theorem of Riemann-Stieltjes Integral
In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15],...
The best possible unification for any collection of physical theories.
The calculus of an unnormalized relational model of data
The catgorical theory of self-similarity.
The classical decision problem and partial functions.