The author proposes bridging disparate explications of sentential connectives (operators). Logicians take sentential operators to denote truth functions and distinguish 16 such binary operators. On the other hand, linguists recognize much more sentential operators and, even for the same truth function, distinguish several connectives with different properties. For example, the conjunction “and” can in some uses have an adversative or conditional or restrictive feature, and sometimes has a temporal or causal meaning. The author favors logico-semantic tools over pragmatic ones and proposes distinguishing operators as truth-functions from complex constructions of truth-functions. The same truth function can be constructed in different ways, which enables one to explain the different properties of a single connective discussed by linguists. The author proposes two conditional connectives – namely one for the necessary conditional relations and another for the sufficient conditional relation – the negation and the logical conjunction as the basic operators. Using these simple connectives, he defines constructions of other sentential operators and demonstrates their various properties.