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...

The Oleinik inequality for conservation laws and AronsonBenilan type inequalities for porous medium or p-Laplacian equations are one-sided inequalities that provide the fundamental features of the solution such as the uniqueness and sharp regularity. In this paper such one-sided inequalities are unified and generalized for a wide class of first and second order equations in the form of ut = σ(t...

This paper gives an explication of our intuitive notion of strength of justification in a controversial debate. It defines a thesis’ degree of justification within the bipolar argumentation framework of the theory of dialectical structures as the ratio of coherently adoptable positions according to which that thesis is true over all coherently adoptable positions. Broadening this definition, th...

We study the expressive power of fragments of inclusion and independence logic defined by restricting the number k of universal quantifiers in formulas. Assuming the so-called strict semantics for these logics, we relate these fragments of inclusion and independence logic to sublogics ESOf (k∀) of existential second-order logic, which in turn are known to capture the complexity classes NTIMERAM...