A complete axiom system for the weak monadic second order theory of two successor funct ions , W2S , is presen ted . The axiom system consists , rough ly , of the general ized Peano axioms and of an inductile defini t ion of the fini te sets . For the proof , methods of J . R . Buchi and J . Doner are used to obtain a new decision procedure for W2S , whose proofs are easi ly formal ized . Diffe...

A multi-valued choice is weak justi…ed if no chosen alternative is dominated by any other obtainable alternative, and for each discarded alternative there is some chosen alternative which dominates it. This de…nition allows us to build a connection between the behavioral property expressed by the weak axiom of revealed non-inferiority and a weak notion of rationality. Our notion of rationaity i...

We introduce a new choice rule that is based on the evidence that decision makers do not pay attention to all items in a menu. Nevertheless they have an underlying rational preference. The Fuzzy Attention Model (FAM) is characterized by an axiom based on revealed stochastic choice akin to the Strong Axiom of Revealed Preference (SARP). The model helps to introduce novel notions of substitutabil...

This paper shows that many simulation equivalences over processes can be characterised by a single parameterised modal logic formula. For many equivalences there is a parameterised modal logic formula f(t) such that for every pair of processes P and Q, P Q if and only if P j= f(Q). For any speci c P the formula f(P ) becomes a x point formula of the normal modal logic K . Strong bisimulation eq...

We prove that a random choice rule satisfies Luce's Choice Axiom if and only its support is correspondence the Weak of Revealed Preference, thus it consists alternatives are optimal according to some preference, then occurs tie-breaking mechanism among such Renyi's Conditioning Axiom. Our result shows is, in precise formal sense, probabilistic version It supports view his own axiom as “canon ra...

In the class of abelian groups a subclass of two-divisible-groups is singled out, and in the latter, a subclass of uniquely-two-divisible-groups. With every such a group a special geometrical structure, more precisely the structure of “congruence of vectors” is correlated. The notion of “affine vector space” (denoted by AffVect) is introduced. This term is defined by means of suitable axiom sys...

Two independent equivalence relations are considered for Mealy automata. Simulation equivalence, on the one hand, arises from a new multi-step simulation concept under the constraint that the process of switching from one automaton to the other is reversible. Retiming equivalence, on the other hand, is the congruence induced by the so called sliding axiom in the monoidal category of automata. I...

As mentioned in the Introduction, it has the following goals: to develop the main topics of revealed preference theory (rationality, revealed preference, congruence, consistency) for a large class of fuzzy choice functions, to explore new topics (degree of dominance, similarity, indicators of rationality) specific to a fuzzy approach to choice functions and to show the manner in which some prob...