SCAN
Literature
Abstracts of Publications about SCAN
In chronological order.
by Dov M. Gabbay and Hans Jürgen Ohlbach,
published in Proc. of KR 92 and in the
South African Computer Journal, 1992.
DVI,
PostScript,
BibTeX-Entry
An algorithm is presented which eliminates second-order quantifiers over predicate variables in formulae of type
$\exists P_1 ,..., P_n\ F$ where $F$ is an arbitrary formula of
first--order predicate logic. The resulting formula is equivalent to
the original formula - if the algorithm terminates.
The algorithm can for example be applied to do interpolation, to eliminate the second--order quantifiers in circumscription,
to compute the correlations between structures and power
structures, to compute semantic properties corresponding to Hilbert
axioms in non classical logics and to compute model theoretic
semantics for new logics.
by Chris Brink and Dov M. Gabbay and Hans Jürgen Ohlbach,
forthcoming in a special issue.
A longer version is available as Technical Report MPI-I-93-220,
Max-Planck-Institut für Informatik, Saarbrücken,
Germany, 1993.
DVI,
PostScript,
BibTeX-Entry
Dualities between different theories occur frequently inmathematics and logic ---
between syntax and semantics of a logic, between structures and power
structures, between relations and relational algebras, to name just a few.
In this paper we show for the case of structures and power structures
how corresponding properties of the two related structures can be
computed fully automatically
by means of quantifier elimination algorithms and predicate logic
theorem provers.
We illustrate the method with a large number of examples and we give
enough technical hints to enable the reader who has access to the {\sc
Otter} theorem prover
to experiment herself.
by Andreas Herzig,
Technical Report MPI-I-96-2-007,
Max-Planck-Institut für Informatik,
Saarbrücken, September 1996.
PostScript,
BibTeX-Entry
The SCAN algorithm has been proposed for second order quantifier
elimination.
In particular it can be applied to find correspondence axioms for
systems of
modal logic.
Up to now, what has been studied are systems with unary modal operators. 17
In this paper we study how SCAN can be applied to various systems
of conditional
logic, which are logical systems with binary modal operators.
by Hans Jürgen Ohlbach.
In McRobbie, M. A. and Slaney, J. K. (eds.),
Automated Deduction: CADE-13.
Lecture Notes in Artificial Intelligence 1104, Springer, 161-165, 1996.
HDVI,
PostScript,
BibTeX-Entry
by Thorsten Engel.
Diplomarbeit, Fachbereich Informatik, Univ. des Saarlandes,
Saarbrücken, October 1996.
HDVI,
PostScript,
BibTeX-Entry
by J.-P. Bodeveix and M. Filali.
Technical Report IRIT-97-44-R, Institut de Recherche en Informatique de
Toulouse, October 1997.
PostScript
by V. Goranko, U. Hustadt, R. A. Schmidt and D. Vakarelov
published in Proceedings of
Relational and Kleene-Algebraic Methods in Computer Science (RelMiCS 7).
Lecture Notes in Computer Science
3051,
Springer,
149-162
(2004).
BiBTeX,
PDF.
SCAN is an algorithm for reducing monadic existential second-order logic
formulae to equivalent simpler formulae, often first-order logic
formulae. It is provably impossible for such a reduction to first-order
logic to be always successful, even if there is an equivalent
first-order formula for a second-order logic formula. In this paper we
show that SCAN successfully computes the first-order equivalents of all
Sahlqvist formulae in the classical (multi-)modal language.
by D. M. Gabbay, R. A. Schmidt, and A. Szalas.
Studies in Logic: Mathematical Logic and Foundations,
Vol. 12,
College Publications
(2008).
ISBN 978-1-904987-56-7.
BiBTeX,
Backcover,
Publisher's info.
Order at amazon.co.uk,
Order at amazon.com,
Order at amazon.de.
|
In recent years there has been an increasing use of logical
methods and significant new developments have been spawned in several
areas of computer science, ranging from artificial intelligence and
software engineering to agent-based systems and the semantic web.
In the investigation and application of logical methods there is
a tension between:
-
the need for a representational language strong enough to express domain
knowledge of a particular application, and
the need for a logical formalism general enough to unify several
reasoning facilities relevant to the application, on the one hand, and
-
the need to enable computationally feasible reasoning facilities,
on the other hand.
|
Second-order logics are very expressive and allow us to represent domain
knowledge with ease, but there is a high price to pay for
the expressiveness.
Most second-order logics are incomplete and highly undecidable.
It is the quantifiers which bind relation symbols that make second-order
logics computationally unfriendly.
It is therefore desirable to eliminate these second-order quantifiers,
when this is mathematically possible; and often it is.
If second-order quantifiers are eliminable we want to know under
which conditions, we want to understand the principles and
we want to develop methods for second-order quantifier elimination.
This book provides the first comprehensive, systematic and uniform
account of the state-of-the-art of second-order quantifier elimination
in classical and non-classical logics.
It covers the foundations, it discusses in detail existing second-order
quantifier elimination methods, and it presents numerous
examples of applications and non-standard uses in different areas.
These include:
-
classical and non-classical logics,
-
correspondence and duality theory,
-
knowledge representation and description logics,
-
commonsense reasoning and approximate reasoning,
-
relational and deductive databases, and
-
complexity theory.
The book is intended for anyone interested in the theory and
application of logics in computer science and artificial intelligence.
SCAN Home
Forms:
Basic Form |
Correspondences Form |
Circumscription Form |
Help
Documentation:
Theory |
Computing Correspondences |
Computing Circumscription |
The System |
Conventions |
Syntax |
Literature
Maintained by
schmidt@cs.man.ac.uk.
Last modified: 05 Aug 13