Substructural Fuzzy-Relevance Logic

Substructural Fuzzy-Relevance Logic

This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, i.e., Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm (based) systems introduced by...

Chapter 3 Substructural logic

Linear logic is the most famous of the substructural logics. Traditional intuitionistic logic, which we call persistent to emphasize the treatment of truth as a persistent and reusable resource, admits the three so-called structural rules of weakening (premises need not be used), contraction (premises may be used multiple times) and exchange (the ordering of premises are irrelevant). Substructu...

Substructural fuzzy logics

A Useful Substructural Logic

Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many diierent ways. They map out structures that are relevant to a number o...

A Substructural Epistemic Resource Logic

We present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents’ local resources. The new modalities can be seen as generalizations of the usual epistemic modalities. The logic combines Boolean BI’s resource semantics with epistemic agency. We give a labelled tableaux calculus and establish soundness and completeness with respect to ...