We develop a general study of the algebraic specification practice, originating from the OBJ tradition, which encodes atomic sentences in logical specification languages as Boolean terms. This practice originally motivated by operational aspects, but also leading to significant increase in expressivity power, has recently become important within the context of some formal verification methodologies mainly because it allows the use of simple equational reasoning for frameworks based on logics that do not have an equational nature. Our development includes a generic rigorous definition of the logics underlying the above mentioned practice, based on the novel concept of ‘quasi-Boolean encoding’, a general result on existence of initial semantics for these logics, and presents a general method for employing Birkhoff calculus of conditional equations as a sound calculus for these logics. The high level of generality of our study means that the concepts are introduced and the results are obtained at the level of abstract institutions (in the sense of Goguen and Burstall [12]) and are therefore applicable to a multitude of logical systems and environments.

Abstract: Many computer science applications concern properties that are true for a restricted class of models. In this paper, a couple of constructor-based institutions are presented. These institutions are defined on top of some base institutions, roughly speaking, by enhancing the syntax with constructor symbols and restricting the semantics to models with elements that are reachable by constructors. The proof rules for the constructor-based Horn logics, formalized as institutions, are defined in this paper, and a proof of completeness is provided in the abstract framework of institutions.

1 Introduction Programming is difficult, as shown by the fact that debugging a program usually takes more time than creating it; moreover, the difficulty of debugging increases non-linearly with program size. One reason for such phenomena is the astonishing complexity and subtlety of the semantics of most widely used programming languages, due mainly to the desire for high efficiency on conventional processors. But rapid increases in the power and flexibility of hardware, and in the need for greater reliability and security in applications, suggest that it may be valuable to consider alternative approaches, based on higher level languages with much simpler semantics, despite the undoubted inertia of tradition, and the difficulty of learning new languages and new paradigms. This paper focuses on the OBJ family of languages, which have semantics based on various extensions of (first order) equational logic. The OBJ languages are logical programming languages, in which programs are theories, and computation is deduction, which makes it possible to do specification, programming and verification in a unified framework. This paper is mainly intended to introduce and motivate the material that it covers, rather than to provide a thorough mathematical exposition. Consequently, there are many references and several examples, but all proofs and many technical details are omitted.

Abstract. The OTS/CafeOBJ method is an instance of the proof score approach to systems analysis, which has been mainly devoted by re-searchers in the OBJ community. We describe some tips on writing proof scores in the OTS/CafeOBJ method and use a mutual exclusion proto-col to exemplify the tips. We also argue soundness of proof scores in the OTS/CafeOBJ method. 1