b) moderate stochastic transitivity: For a reciprocal fuzzy relation Q : x2 + [O, 11 on a finite set of alternatives X , we introduce the concept of U-transitivity which is based upon the ordering of the matrix elements qij, qjk and qki of Q for all triples of indices i, j and k. We show that U-transitivity generalizes both stochastic and fuzzy transitivity. The U-transitivity of the secalled u...

Recently, we introduced the framework of cycletransitivity as a general means of representing transitivity conditions on reciprocal relations. In this framework, for reciprocal relations, the concepts of T -transitivity and stochastic transitivity can be cast. The upper bound functions encountered in this framework for product-transitivity and dice-transitivity, conceptually related to the prob...

In a response to Block and Barnett (2012), this paper clarifies some misunderstandings about the concept of transitivity and shows its relation to rationality, asynchronicity of choice, and indifference analysis. It is demonstrated that Block and Barnett, contrary to their self-interpretation, do not in fact attack transitivity but the assumption of stable preferences. It is argued that the sta...

We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, together with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is strictly weaker than transitivity but in the case of collective choice rules that satisfy further properties, the conjunctio...

In response to Block and Barnett (2012), this paper clarifies some misunderstandings about the concept of transitivity and shows its relation to rationality, asynchronicity of choice, and indifference analysis. It is demonstrated that Block and Barnett, contrary to their self-interpretation, do not in fact attack transitivity but the assumption of stable preferences. It is argued that the stabi...

Systemic Functional Linguistics provides a semiotic perspective on language. The text analysis described in Systemic Functional Linguistics (SFL) can be of critical value in real-world applications. But parsing with SFL grammars is computationally intensive task and parsers for this level of description to date have not been able to operate on unrestricted input. This paper describes a graph-ba...