On representations of logics
On Rough Subgroup of a Group
This article describes a rough subgroup with respect to a normal subgroup of a group, and some properties of the lower and the upper approximations in a group.
On Semantics of a Term Calculus for Classical Logic
On sequent calculi for intuitionistic propositional logic
The well-known Dyckoff's 1992 calculus/procedure for intuitionistic propositional logic is considered and analyzed. It is shown that the calculus is Kripke complete and the procedure in fact works in polynomial space. Then a multi-conclusion intuitionistic calculus is introduced, obtained by adding one new rule to known calculi. A simple proof of Kripke completeness and polynomial-space decidability of this calculus is given. An upper bound on the depth of a Kripke counter-model is obtained.
On some conjectures connected with complete sentences
On some contributions to quantum structures by fuzzy sets
It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.
On some Generalizations of a Class of Discrete Functions
In this paper we examine discrete functions that depend on their variables in a particular way, namely the H-functions. The results obtained in this work make the “construction” of these functions possible. H-functions are generalized, as well as their matrix representation by Latin hypercubes.
On some inexact relations in probabilized Boolean algebras.
This paper is devoted to characterize monotonicity, conditionality and transitivity of some rational relations defined in a probabilized Boolean Algebra.
On some properties of grounding nonuniform sets of modal conjunctions
A language grounding problem is considered for nonuniform sets of modal conjunctions consisting of conjunctions extended with more than one modal operator of knowledge, belief or possibility. The grounding is considered in the context of semiotic triangles built from language symbols, communicative cognitive agents and external objects. The communicative cognitive agents are assumed to be able to observe external worlds and store the results of observations in internal knowledge bases. It is assumed...
On some properties of transformations of a logic
On Square-Free Numbers
In the article the formal characterization of square-free numbers is shown; in this manner the paper is the continuation of [19]. Essentially, we prepared some lemmas for convenient work with numbers (including the proof that the sequence of prime reciprocals diverges [1]) according to [18] which were absent in the Mizar Mathematical Library. Some of them were expressed in terms of clusters’ registrations, enabling automatization machinery available in the Mizar system. Our main result of the article...
On the Algebraic Complexity of Sets of Functions
On the axiomatisation of Boolean categories with and without medial.
On the Axiomatizability of Certain Classes of Modules.
On the Beth property in extension of Lukasiewicz logics.
On the categorical semantics of elementary linear logic.
On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices
Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude that the...
On the constructions of t-norms and t-conorms on some special classes of bounded lattices
Recently, the topic related to the construction of triangular norms and triangular conorms on bounded lattices using ordinal sums has been extensively studied. In this paper, we introduce a new ordinal sum construction of triangular norms and triangular conorms on an appropriate bounded lattice. Also, we give some illustrative examples for clarity. Then, we show that a new construction method can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on...
On the decidability of p', p'' and p''*.
On the decidability of semigroup freeness∗
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....