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Titlebook: Labelled Non-Classical Logics; Luca Viganò Book 2000 Springer Science+Business Media Dordrecht 2000 calculus.complexity.modal logic.proof.

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发表于 2025-3-21 19:00:01 | 显示全部楼层 |阅读模式
书目名称Labelled Non-Classical Logics
编辑Luca Viganò
视频video
图书封面Titlebook: Labelled Non-Classical Logics;  Luca Viganò Book 2000 Springer Science+Business Media Dordrecht 2000 calculus.complexity.modal logic.proof.
描述I am very happy to have this opportunity to introduce Luca Vigano‘s book on Labelled Non-Classical Logics. I put forward the methodology of labelled deductive systems to the participants of Logic Colloquium‘90 (Labelled Deductive systems, a Position Paper, In J. Oikkonen and J. Vaananen, editors, Logic Colloquium ‘90, Volume 2 of Lecture Notes in Logic, pages 66-68, Springer, Berlin, 1993), in an attempt to bring labelling as a recognised and significant component of our logic culture. It was a response to earlier isolated uses of labels by various distinguished authors, as a means to achieve local proof­ theoretic goals. Labelling was used in many different areas such as resource labelling in relevance logics, prefix tableaux in modal logics, annotated logic programs in logic programming, proof tracing in truth maintenance systems, and various side annotations in higher-order proof theory, arithmetic and analysis. This widespread local use of labels was an indication of an underlying logical pattern, namely the simultaneous side-by-side manipulation of several kinds of logical information. It was clear that there was a need to establish the labelled deductive systems methodology.
出版日期Book 2000
关键词calculus; complexity; modal logic; proof; proof theory
版次1
doihttps://doi.org/10.1007/978-1-4757-3208-5
isbn_softcover978-1-4419-4962-2
isbn_ebook978-1-4757-3208-5
copyrightSpringer Science+Business Media Dordrecht 2000
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发表于 2025-3-21 20:40:52 | 显示全部楼层
发表于 2025-3-22 01:56:19 | 显示全部楼层
Labelled Natural Deduction Systems for Propositional Modal Logicsstems with inheritance of theorems. Moreover, it allows modular proofs of metatheoretical properties, in that these proofs, along with the presentations themselves, are parameterized over the properties of the relations.
发表于 2025-3-22 05:46:09 | 显示全部楼层
Labelled Natural Deduction Systems for Propositional Non-Classical Logicsnt of a wide range of non-classical operators (□, ◊, relevant and intuitionistic implication, non-classical negation, etc.), where we base our presentations on an abstract classification of non-classical operators as ‘universal’ or ‘existential’, and associated general metatheorems. We proceed as follows.
发表于 2025-3-22 10:19:03 | 显示全部楼层
发表于 2025-3-22 15:50:29 | 显示全部楼层
Labelled Natural Deduction Systems for Quantified Modal Logicsarbitrarily (varying domains), or do the same objects exist in every world (constant domains), or are objects possibly created (increasing domains) or destroyed (decreasing domains) when moving to accessible worlds?
发表于 2025-3-22 17:52:04 | 显示全部楼层
Discussionhierarchical structuring), and have modular metatheoretical properties, in particular soundness and completeness, and normalization of derivations and a subformula property, which we can exploit to delineate advantages and limitations of our approach..
发表于 2025-3-23 00:25:55 | 显示全部楼层
Complexity of Proof Search in K, T, K4 and S4ned with the soundness and completeness of our systems with respect to the corresponding Kripke semantics, tell us that the provability (validity) problems for the modal logics K, T, K4 and S4 are decidable in PSPACE.
发表于 2025-3-23 01:34:07 | 显示全部楼层
Discussionbounds by combining restrictions on the structural rules of our labelled sequent systems with an analysis of the accessibility relation of the corresponding Kripke frames. Furthermore, we have shown that as a by-product of our analysis we can obtain justifications (and in some cases refinements) of the rules of standard sequent systems.
发表于 2025-3-23 08:50:17 | 显示全部楼层
Introduction and Preliminariesr all logics in the family, and a labelling algebra, which we extend to generate systems for particular logics. Now we use our framework to develop a proof-theoretical method for bounding the computational complexity of the decision problem for a number of these logics.
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