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Geometric Rules in Infinitary Logic
2021Large portions of mathematics such as algebra and geometry can be formalized using first-order axiomatizations. In many cases it is even possible to use a very well-behaved class of first-order axioms, namely, what are called coherent or geometric implications.
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Complete Infinitary Type Logics
Studia Logica, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Chain Logic and Shelah's Infinitary Logic
2019This version is the final autors' version.
D��amonja, Mirna +1 more
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Hybrid Logics with Infinitary Proof Systems
Journal of Logic and Computation, 2006We provide a strongly complete infinitary proof system for hybrid logic. This proof system can be extended with countably many sequents. Thus, although these logics may be non-compact, strong completeness proofs are provided for infinitary hybrid versions of non-compact logics like ancestral logic and Segerberg's modal logic with the bounded chain ...
Kooi, Barteld +2 more
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1994
It is known that a theory in S5-epistemic logic with several agents may have numerous models. This is because each such model specifies also what an agent knows about infinite intersections of events, while the expressive power of the logic is limited to finite conjunctions of formulas.
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It is known that a theory in S5-epistemic logic with several agents may have numerous models. This is because each such model specifies also what an agent knows about infinite intersections of events, while the expressive power of the logic is limited to finite conjunctions of formulas.
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2018
An infinitary logic arises from ordinary first-order logic when one or more of its finitary properties is allowed to become infinite, for example, by admitting infinitely long formulas or infinitely long or infinitely branched proof figures. The need to extend first-order logic became pressing in the late 1950s when it was realized that many of the ...
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An infinitary logic arises from ordinary first-order logic when one or more of its finitary properties is allowed to become infinite, for example, by admitting infinitely long formulas or infinitely long or infinitely branched proof figures. The need to extend first-order logic became pressing in the late 1950s when it was realized that many of the ...
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Supervenience and Infinitary Logic
Noûs, 2001Etude de l'interaction entre la survenance et la logique infinie. Examinant l'usage restreint et l'usage non restreint de la logique infinie, ainsi que les problemes metaphysiques qui en resultent, l'A. met en evidence les dangers de la cloture infinie, et montre que la logique infinie souleve un nouveau paradoxe concernant le statut physique de l ...
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From finitary to infinitary second‐order logic
Mathematical Logic Quarterly, 2005AbstractA back and forth condition on interpretations for those second‐order languages without functional variables whose non‐logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language.
Weaver, George, Penev, Irena
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Journal of Symbolic Logic, 1976
This paper is concerned with the proof theoretic development of certain infinite languages. These languages contain the usual infinite conjunctions and disjunctions, but in addition to homogeneous quantifiers such as ∀x0x1x2 … and ∃y0y1y2 …, we shall investigate particular subclasses of the dependent quantifiers described by Henkin [1].
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This paper is concerned with the proof theoretic development of certain infinite languages. These languages contain the usual infinite conjunctions and disjunctions, but in addition to homogeneous quantifiers such as ∀x0x1x2 … and ∃y0y1y2 …, we shall investigate particular subclasses of the dependent quantifiers described by Henkin [1].
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Infinitary propositional normal modal logic
Studia Logica, 1987The author introduces a propositional normal modal logic, denoted by \(KL_{\omega_ 1}\), with countable conjunction and disjunction. He gives the Hilbert type formulation of \(KL_{\omega_ 1}\), defines the class of Kripke frames characteristic for this logic (completeness theorem) and proves that \(KL_{\omega_ 1}\) has the Craig interpolation property.
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