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Reflecting our experiences in areas, like Algebraic Specifications, AbstractModel Theory, Graph Transformations, and Model Driven Software Engineering(MDSE), we present a general, category independent approach to Logics ofFirst-Order Constraints (LFOC). Traditional First-Order Logic, DescriptionLogic and the sketch framework are discussed as examples. We use the concept ofinstitution [Diaconescu08,GoguenBurstall92] as a guideline to describe LFOC's.The main result states that any choice of the six parameters, we are going todescribe, gives us a corresponding "institution of constraints" at hand. The"presentations" for an institution of constraints can be characterized as"first-order sketches". As a corresponding variant of the "sketch-entailments"in [Makkai97], we finally introduce "sketch rules" to equip LFOC's with thenecessary expressive power.

Logics of First-Order Constraints -- A Category Independent Approach