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Tarskian Structured Consequence Relations and Functional Completeness,ent-style proof-theoretic semantics, see e.g. , , , , , and . The idea now is to apply this kind of approach to Gabbay’s notion of a Tarski-type . |~ between structured databases Δ and single formulas .. This concept generalizes the ordinary notion of single-conclusion调色板 发表于 2025-3-25 14:12:24
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Predicate Logics on Display,logics obtained by adopting van Benthem’s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap’s display logic, . by introduction rules for the existential and the universal quantifier. These rules for ∀. and ∃. are analogous to the display introremission 发表于 2025-3-26 06:04:35
Appendix, a sequent calculus presentation. Usually, this is a rather fortunate situation. It may happen that certain axiom schemata are characterizable by algebraic or relational properties expressible in an interesting fragment of first-order logic, and that Gentzen-style proof systems lend themselves to auexorbitant 发表于 2025-3-26 10:46:06
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Predicate Logics on Display,duction rules for the modal operators □ and ◊ and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal ‘modal’ predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. The chapter has two main aims, namelySAGE 发表于 2025-3-26 17:03:33
Book 1998essfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen‘s sequent calculus developed by Nuel D. Belnap. This book is far from of