We study a process calculus which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s probabilistic automata. We consider various strong and weak behavioral equivalences, and we provide complete axiomatizations for finite-state processes, restricted to guarded definitions in case of the weak equivalences. We conjecture that in the general case of unguard...

Formal symptoms of relevance usually concern the propositional variables shared between antecedent and consequent provable conditionals. Among most famous results about such are Belnap’s early showing that for sublogics strong relevant logic R, conditionals share a signed variable consequent. For logics weaker than R stronger sharing available. In 1984, Ross Brady gave one well-known example re...

The standard use of the propositional calculus ('P.C.') in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be 'safely' used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions...

In this paper we prove an existence of some type of equivalences between triangulated categories of singularities for varieties of different dimensions. This class of equivalences generalizes so called Knörrer periodicity. As consequence we get equivalences between categories of D-branes of type B on Landau-Ginzburg models of different dimensions.