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General logics
 In Logic Colloquium 87
, 1989
"... theory, categorical logic. model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms repre ..."
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theory, categorical logic. model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum
An institutional view on categorical logic and the CurryHowardTaitisomorphism
"... We introduce a generic notion of propositional categorical logic and provide a construction of an institution with proofs out of such a logic, following the CurryHowardTait paradigm. We then prove logicindependent soundness and completeness theorems. The framework is instantiated with a number ..."
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We introduce a generic notion of propositional categorical logic and provide a construction of an institution with proofs out of such a logic, following the CurryHowardTait paradigm. We then prove logicindependent soundness and completeness theorems. The framework is instantiated with a number of examples: classical, intuitionistic, linear and modal propositional logics. Finally, we speculate how this framework may be extended beyond the propositional case.
Heterogeneous Theories and the Heterogeneous Tool Set
"... Heterogeneous multilogic theories arise in different contexts: they are needed for the specification of large software systems, as well as for mediating between different ..."
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Heterogeneous multilogic theories arise in different contexts: they are needed for the specification of large software systems, as well as for mediating between different
What is a Logic? In memoriam Joseph Goguen
"... model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A ..."
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model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum