On the strength of several versions of Dirichlet's ("Pigeon-Hole"-) principle in the sense of first-order logic.
On the structure and classification of SOMAs: Generalizations of mutually orthogonal Latin squares.
On the structure of continuous uninorms
Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation in the unit interval with the neutral element . If operation is continuous, then or . So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element , which is continuous in the open unit square may be given in ...
On the structure of intuitionistic algebras with relational probabilities.
Trillas ([1]) has defined a relational probability on an intuitionistic algebra and has given its basic properties. The main results of this paper are two. The first one says that a relational probability on a intuitionistic algebra defines a congruence such that the quotient is a Boolean algebra. The second one shows that relational probabilities are, in most cases, extensions of conditional probabilities on Boolean algebras.
On the structure of numerical event spaces
The probability of the occurrence of an event pertaining to a physical system which is observed in different states determines a function from the set of states of the system to . The function is called a numerical event or multidimensional probability. When appropriately structured, sets of numerical events form so-called algebras of -probabilities. Their main feature is that they are orthomodular partially ordered sets of functions with an inherent full set of states. A classical...
On the structure of perfect sets in various topologies associated with tree forcings
We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.
On the sum of observables in a logic
On the syntactico-semantical completeness of first-order fuzzy logic. I. Syntax and semantics
On the syntactico-semantical completeness of first-order fuzzy logic. II. Main results
On the -conditionality of -power based implications
It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of -conditionality. In this paper, the -conditionality for -power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication being -conditional are obtained. Moreover, the sufficient conditions under which a power based implication is -conditional are discussed, this discussions give an...
On the t-closure Condition of Martin.
On the tensor product of a Boolean algebra and an orthoalgebra
On the theory of grossone.
On the topological complexity of infinitary rational relations
We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [20].
On the Topological Complexity of Infinitary Rational Relations
We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [20].
On the transfer principle in fuzzy theory.
We show in this paper that almost all results proved in many papers about fuzzy algebras can be proved uniformly and immediately by using so-called Transfer Principle.
On the uniqueness problem for quite full logics
On the weak pigeonhole principle
We investigate the proof complexity, in (extensions of) resolution and in bounded arithmetic, of the weak pigeonhole principle and of the Ramsey theorem. In particular, we link the proof complexities of these two principles. Further we give lower bounds to the width of resolution proofs and to the size of (extensions of) tree-like resolution proofs of the Ramsey theorem. We establish a connection between provability of WPHP in fragments of bounded arithmetic and cryptographic assumptions (the existence...
On the weak representability of -complete dimension complemented cylindric algebras
On the -superposition of functions of a -valued logic.