Models of linear logic
Model-theoretic properties of cause-and-effect structures
Modified modus ponens and modal logic
Modules over a quantale and models for the operator in linear logic
Molecules and linerly ordered ideals of MV-algebras.
We show that an ideal I of an MV-algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I ≠ {0} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combinations of the properties of being implicative, essential, weakly essential, maximal or prime.
Monotone (co)inductive types and positive fixed-point types
Monotone (co)inductive types and positive fixed-point types
We study five extensions of the polymorphically typed lambda-calculus (system F) by type constructs intended to model fixed-points of monotone operators. Building on work by Geuvers concerning the relation between term rewrite systems for least pre-fixed-points and greatest post-fixed-points of positive type schemes (i.e., non-nested positive inductive and coinductive types) and so-called retract types, we show that there are reduction-preserving embeddings even between systems of monotone (co)inductive...
More on Divisibility Criteria for Selected Primes
This paper is a continuation of [19], where the divisibility criteria for initial prime numbers based on their representation in the decimal system were formalized. In the current paper we consider all primes up to 101 to demonstrate the method presented in [7].
Morley’s Trisector Theorem
Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
MV-algebras with additive closure operators
Natural deduction and sequent typed lambda calculus.
Natural limitations of decisions procedures for arithmetic with bounded quantifiers.
Natural Numbers In Illative Combinatory Logic.
N-Dimensional Binary Vector Spaces
The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields and n-dimensional...
Negation And Contradiction.
Negative Modal Operators in Intuitionistic Logic
Negative modal operators in intuitionistic logic.
Několik cest k minimalizaci výrokových forem
New applications of the wreath product of forest algebras
We give several new applications of the wreath product of forest algebras to the study of logics on trees. These include new simplified proofs of necessary conditions for definability in CTL and first-order logic with the ancestor relation; a sequence of identities satisfied by all forest languages definable in PDL; and new examples of languages outside CTL, along with an application to the question of what properties are definable in both CTL and LTL.
New kinds of hybrid filters of EQ-algebras
The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed and it is...