In this paper, we consider a set of quite interesting three- and four-valued logics prove the normalisation theorem for their natural deduction formulations. Among in question are Logic Paradox, First Degree Entailment, Strong Kleene logic, some implicative extensions, including RM3 RM3⊃. Also, present detailed version Prawitz’s proof Nelson’s logic N4 its extension by intuitionist negation.

Within the program of finding axiomatizations for various parts of computability logic, an earlier article proved that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort of reduction permits unlimited reusage of the computational resource represented by the antecedent. An at least equally basic and natural sort of algori...

A b s t r a c t. The paper deals with functional properties of three-valued logics. We consider the family of regular three-valued Kleene's logics (strong, weak, intermediate) and it's extensions by adding an implicative connectives (" natural " implications). The main result of our paper is the lattice that describes the relations between implicative extensions of regular logics. In this paper...

The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships between these filters and quotient algebras that are constructed via these filters are described....

The articles [11], [7], [13], [1], [14], [5], [6], [4], [9], [10], [15], [16], [12], [2], [3], and [8] provide the notation and terminology for this paper. Let us note that every lower bound lattice which is Heyting is also implicative and every lattice which is implicative is also upper-bounded. In the sequel T denotes a topological space and A, B denote subsets of the carrier of T . The follo...

Implicative statistics criteria have proven to be valuable interestingness measures for association rules. Here we highlight their interest for classification trees. We start by showing how Gras’ implication index may be defined for rules derived from an induced decision tree. This index is especially helpful when the aim is not classification itself, but characterizing the most typical conditi...

Within the program of finding axiomatizations for various parts of computability logic, an earlier article proved that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort of reduction permits unlimited reusage of the computational resource represented by the antecedent. An at least equally basic and natural sort of algori...

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

Several other chapters in this book analyze grammatical phenomena according to the architectural assumptions and constraint-based representational apparatus of lexicalist theories of grammar; in the present chapter, we ask some fundamental questions concerning what it means for a theory to be lexicalist. While critically assessing some consensus beliefs among lexicalists, this exploration will ...

(Ackerman et al., 2009) go on to argue that speakers rely on knowledge of the IMPLICATIVE STRUCTURE of paradigms (Wurzel, 1984): paradigms are structured in such a way that there are reliable correlations between the form filling one paradigm cell A and the form filling another cell B. The reliability of these correlations depends on the particular pair of cells A and B under scrutiny; it can b...