Separating minimal, intuitionist, and classical logic.

Minimal Classical Logic and Control Operators

Strong Paraconsistency by Separating Composition and Decomposition in Classical Logic

In this paper I elaborate a proof system that is able to prove all classical first order logic consequences of consistent premise sets, without proving trivial consequences of inconsistent premises (as in A,¬A ` B). Essentially this result is obtained by formally distinguishing consequences that are the result of merely decomposing the premises into their subformulas from consequences that may ...

Embedding classical in minimal implicational logic

Consider the problem which set V of propositional variables suffices for StabV `i A whenever `c A, where StabV := {¬¬P → P | P ∈ V }, and `c and `i denote derivability in classical and intuitionistic implicational logic, respectively. We give a direct proof that stability for the final propositional variable of the (implicational) formula A is sufficient; as a corollary one obtains Glivenko’s t...

Separating Quantum and Classical Learning

We consider a model of learning Boolean functions from quantum membership queries. This model was studied in [26], where it was shown that any class of Boolean functions which is information-theoretically learnable from polynomially many quantum membership queries is also information-theoretically learnable from polynomially many classical membership queries. In this paper we establish a strong...

Minimal Separating Sets for

For a Muller automaton only a subset of its states is needed to decide whether a run is accepting or not: The set I the innnitely often visited states can be replaced by the intersection I \ W with a xed set W of states, provided W is large enough to distinguish between accepting and non-accepting loops in the automaton. We call such a subset W a separating set. Whereas the idea was previously ...