Using Gärdenfors’s notion of epistemic entrenchment, we develop the semantics of a logic which accounts for the following points. It explains why we may generally infer If ¬A then B if all we know is A∨B while must not generally infer If ¬A then B if all we know is {A∨B,A}. More generally, it explains the nonmonotonic nature of the consequence relation governing languages which contain conditio...

We consider the generating function for a q-analogue of non-strict multiple zeta values (or multiple zeta-star values) and prove an explicit formula for it in terms of a basic hypergeometric series 3φ2. By specializing the variables in the generating function, we reproduce the sum formula obtained by Ohno and Okuda and get some relations in the case of full height.

In this paper we present asymptotic expressions for the number of functions satisfying the Strict Avalanche Criterion (SAC) with respect to one and two variables, previously developed by O’Connor. Cusick recently gave a conjecture for a lower bound on the number of functions satisfying the SAC. Here, we give a constructive proof for this conjecture. Moreover, we provide an improved lower bound.

It is shown that the notion of conditional possibility can be consistently introduced in possibility theory, in very much the same way as conditional expectations and probabilities are defined in the measureand integral-theoretic treatment of probability theory. I write down possibilistic integral equations which are formal counterparts of the integral equations used to define conditional expec...