In this chapter we first give a model theoretic presentation of classical first order logic with equality and show the invariance of the satisfaction relation between models and sentences with respect to the change of notation. This is our first example of an institution. We then introduce the abstract concept of institution and illustrate it by a list of examples from logic and computing science. The next section introduces morphisms and comorphisms of institutions, which are mappings preserving the structure of institution with rather complementarymeaning in the actual situations. The final section of this chapter, which is intended for the more category theoretic minded readers, provides a more categorical definition for the concept of institution, which eases considerably our access to the structural properties of categories of institutions. As an application we prove the existence of limits of institutions
KeywordsPropositional Logic Kripke Model Satisfaction Condition Heyting Algebra Relation Symbol
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