The Conjunction and Disjunction Theses

Combining Conjunction with Disjunction

In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, di...

Generalized conjunction/disjunction

The generalized conjunction/disjunction function (GCD) is a continuous logic function of two or more variables that integrates conjunctive and disjunctive properties in a single function. It is used as a mathematical model of simultaneity and replaceability of inputs. Special cases of this function include the full (pure) conjunction, the partial conjunction, the arithmetic mean, the partial di...

Deriving Non-determinism from Conjunction and Disjunction

In this paper, we show that the non-deterministic choice “+”, which was proposed as a primitive operator in Synchronization Tree Logic (STL for short) can be defined essentially by conjunction and disjunction in the μ-calculus (μM for short). This is obtained by extending the μcalculus with the non-deterministic choice “+” (denoted by μM) and then showing that μM can be translated into μM. Furt...

Properties and Modeling of Partial Conjunction/Disjunction

The partial conjunction/disjunction function (PCD) integrates conjunctive and disjunctive features in a single function. Special cases of this function include the pure conjunction, the pure disjunction, and the arithmetic mean. PCD enables a continuous transition from the pure conjunction to the pure disjunction, using a parameter that specifies a desired level of conjunction (andness) or disj...

Addition of fuzzy quantities: Disjunction-conjunction approach