Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with res...

The purpose of this note is the study of L-multialgebras and fuzzy congruences of multialgebras. In this regards first the notion of a L-multialgebras are introduced and studied and then the notion of a P -fuzzy relations on multialgebra are given and is applied to introduce the notion of P -fuzzy congruence of multialgebras. Finally, the lattices of P -fuzzy (resp. strong) congruences of multi...

Weak relative pseudocomplementation on a meet semilattice S is a partial operation ∗ which associates with every pair (x, y) of elements, where x ≥ y, an element z (the weak pseudocomplement of x relative to y) which is the greatest among elements u such that y = u ∧ x. The element z coincides with the pseudocomplement of x in the upper section [y) and, if S is modular, with the pseudocomplemen...

We discuss a new type of weak factorization system. Although these systems provide (up to isomorphism) uniquely determined decompositions of morphisms, in general they do not constitute orthogonal factorizations and are not even functorial. Nevertheless, they arise naturally, as injective hulls or projective covers in comma categories. Surprisingly, often injective hulls and projective covers c...

Flat iteration is a variation on the original binary version of the Kleene star operation P Q, obtained by restricting the rst argument to be a sum of atomic actions. It generalizes pre x iteration, in which the rst argument is a single action. Complete nite equational axiomatizations are given for ve notions of bisimulation congruence over basic CCS with at iteration, viz. strong congruence, b...

Matroids over tracts provide an algebraic framework simultaneously generalizing the notions of matroids, oriented and valuated presented by Baker Bowler. Pendavingh partially extended this theory to skew hyperfields a new axiom system in terms quasi-Pl\"ucker coordinates. We present matroids tracts, which generalizes both weak developed Pendavingh. give several cryptomorphic systems for such ci...

This paper provides a fully abstract semantics for valuepassing CCS for trees (VCCTS). The operational semantics is given both in terms of a reduction semantics and in terms of a labelled transition semantics. The labelled transition semantics is non-sequential, allowing more than one action occurring simultaneously. We develop the theory of behavioral equivalence by introducing both weak barbe...

Synthetic methods in science can aim at either instantiating a target phenomenon or simulating key mechanisms underlying that phenomenon; 'strong' and 'weak' approaches, respectively. While the former assumes a mature theory, the latter find its value in helping specify such theories. Here, we argue that artificial consciousness is best pursued as a (weak) means of theory development in conscio...

This paper studies the extensions of the infinte-horizon variants of the leximin principle and utilitarianism on the set of infinite utility streams. We especially examine those extensions which satisfy the axiom of Preference-continuity (or Consistency) and the extended anonymity axiom called Q-Anonymity. We formulate new extended leximin and utilitarian social welfare relations (SWRs), called...

Lattice Horn sentences including Geyer’s SD(n, 2) and their conjugates C(n, 2) are considered. SD(2, 2) is the meet semidistributivity law SD∧. Both SD(n, 2) and C(n, 2) become strictly weaker when n grows. For varieties V the satisfaction of SD(n, 2) in {Con(A) : A ∈ V} is characterized by a Mal’cev condition. Using this Mal’cev condition it is shown that C(n, 2) |=con SD(n, 2), which means th...