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We review links between three logic formalisms and three approaches to specifying operational semantics. In particular, we show that specifications written with (small-step and big-step) SOS, abstract machines, and multiset rewriting, are closely related to Horn clauses, binary clauses, and (a subset of) linear logic, respectively. We shall illustrate how binary clauses form a bridge between the other two logical formalisms. For example, using a continuation-passing style transformation, Horn clauses can be transformed into binary clauses. Furthermore, binary clauses can be seen as a degenerative form of multiset rewriting: placing binary clauses within linear logic allows for rich forms of multiset rewriting which, in turn, provides a modular, big-step SOS specifications of imperative and concurrency primitives. Establishing these links between logic and operational semantics has many advantages for operational semantics: tools from automated deduction can be used to animate semantic specifications; solutions to the treatment of binding structures in logic can be used to provide solutions to binding in the syntax of programs; and the declarative nature of logical specifications provides broad avenues for reasoning about semantic specifications.