ENGLISH

Displaying Modal Logic

By Wansing H.

Book information

Publisher
Kluwer
Year
1998
ISBN
079235205X, 9780792352051
LCC
BC199.M6 W36 1998
Language
english
Format
DJVU
Filesize
2 MB (1661045 bytes)
Series
Trends in Logic, Volume 3
Pages
265\265
Topic
Mathematics Logic
Library
Kolxo3
DPI
300
Orientation
portrait
Paginated
no
Scanned
yes
Time added
2011-07-22 07:35:22

Description

This is the first comprehensive introduction to Display Logic in the context of generalized Gentzen calculi. After reviewing several standard and non-standard sequent-style proof systems for modal logics, the author carefully motivates and develops Display Logic, an important refinement of Gentzen's sequent calculus devised by N. Belnap. A general strong cut-elimination theorem is proved that covers a large class of display sequent calculi. Moreover, a proof-theoretic semantics of the modal operators is developed. Proof-theoretic characterizations are also obtained for the logical operations of systems associated with Tarskian structured consequence relations. These systems include constructive logics with strong negation. Using the embedding of intuitionistic logic in S4, display calculi are presented for certain subintuitionistic logics that may be used as monotonic base systems for semantics-based non-monotonic reasoning. Eventually, a first-order display calculus is defined. Its modal extension is general enough to avoid the provability of both the Barcan formula and its converse.

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