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Topic: Monadic logic

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	Monadic Second-Order Logic and planar graph drawings with edge crossings: abstract (Site not responding. Last check: 2007-11-07)
		We consider the logical expressibility of the realizability of an arbitrary finite structure of the appropriate type as the representation of a concrete drawing.
		This property is monadic second-order for the structures representing a planar drawing of a planar graph (called the frame) augmented with additional edges that may cross one another and that may cross the edges of the frame.
		Monadic second-order (MS) logic is especially interesting as a logical language for this purpose.
	www.labri.fr /Perso/~courcell/Art13.html (433 words)

	Activités Scientifiques de B. Courcelle
		The monadic second-order logic of graphs V: on closing the gap between definability and recognizability, Vol.
		The monadic second-order logic of graphs XI: Hierarchical decompositions of connected graphs, Theoret.
		Vertex-minors, monadic second-order logic and a conjecture by Seese, with Sang-il Oum (
	www.labri.fr /Perso/~courcell/ActSci.html (1901 words)

	Monad - Definition of Monad by Webster's Online Dictionary (Site not responding. Last check: 2007-11-07)
		monad - / mo ' nad / A technique from category theory which has been adopted as a way of dealing with state in functional programming languages in such a way that the details of the state are hidden or abstracted out of code that merely passes it on unchanged.
		A monad has three components : a means of augmenting an existing type, a means of creating a default value of this new type from a value of the original type, and a replacement for the basic application operator for the old type that works with the new type.
		The alternative to passing state via a monad is to add an extra argument and return value to many functions which have no interest in that state.
	www.webster-dictionary.org /definition/monad (628 words)

	Monadic logic - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-07)
		In mathematics, a monadic logic is one that employs only unary relation s.
		Deductive databases and monadic logic (Rapports de recherche.
		The closure of monadic NP (Research report RJ.
	encyclopedia.worldsearch.com /monadic.htm (38 words)

	SYMBOLIC PROCESSING IN PASCAL - Chapter 15
		In monadic logic it so happens that if a formula is true in all interpretations over finite domains then it is true in all interpretations and hence a logical truth.
		In monadic logic at most finite countermodels are required to show that a given formula is a logical truth or that a given argument is valid.
		In propositional logic an interpretation associates with every atomic proposition a truth value, but an open path in a semantic tableau may leave it undetermined whether a particular atom is to be made true or false.
	www.latrobe.edu.au /philosophy/phimvt/sympas/s33mondef.html (10220 words)

	MONA: Monadic Second-Order Logic in Practice (Site not responding. Last check: 2007-11-07)
		The purpose of this article is to introduce Monadic Second-order Logic as a practical means of specifying regularity.
		The logic is a highly succinct alternative to the use of regular expressions.
		We have built a tool Mona, which acts as a decision procedure and as a translator to finite-state machines.
	www.brics.dk /RS/95/21 (134 words)

	Yuri Gurevich: Annotated Articles
		In that sense, first-order logic is the underlying logic of Hoare logic.
		A logic L is said to capture (or to be tailored to) a complexity class C if a class of finite ordered structures of a fixed vocabulary belongs to C if and only if it is definable in L. Traditionally, complexity tailored logics are logics of relations.
		The zero-one law, known to hold for first-order logic but not for monadic or even existential monadic second-order logic, is generalized to the extension of first-order logic by the least (or iterative) fixed-point operator.
	research.microsoft.com /users/gurevich/annotated.html (11660 words)

	SDRL: Systems Design Research Lab
		In the area of knowledge representation LP allows us to approach classical logical omniscience problem, which addresses a failure of the traditional logic of knowledge to distinguish between given facts, like logical axioms on one hand and knowledge which can be only obtained after a long derivation process.
		We show how the logic can be used to describe the layout of bits in a memory word, the layout of memory words in a region, the layout of regions in an address space, or even the layout of address spaces in a multiprocessing environment.
		The logic is defined appropriately, with layer formulas describing processes within a layer, and temporal formulas describing the sequence of layers in the computation.
	www.cis.upenn.edu /sdrl/seminars.php3 (2939 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Logic}, volume = 13, year = 1978, pages = {171--224} } @inproceedings{BCG92, author = {Th.
		Logic}, volume = 49, year = 1990, pages = {193--255} } @article{Cou91, author = {B. Courcelle}, title = {The monadic second order logic of graphs {V}: on closing the gap between definability and recognizability}, journal = {Theoretical Comput.
		Logic}, volume = 72, year = 1995, pages = {103--143} } @article{Cou95b, author = {B. Courcelle}, title = {The monadic second order logic of graphs {IX}: machine and their behaviours}, journal = {Theoretical Comput.
	www.ldc.usb.ve /~arratia/refs/ALL.bib (1635 words)

	Home Page for Steven Lindell
		I study the logical definability of complexity classes given by models of computation whose resources are bounded by mathematical (or physical) limits.
		Computing monadic fixed-points in linear-time on doubly-linked data structures (Given June 24, 2005 at Seventh International workshop on Logic and Computational Complexity).
		Linear-time algorithms for Monadic Logic (given at the University of Pennsylvania's Logic and Computation Seminar, February 2003) [a shorter version skipping slides 7, 9, 10, 11 was given at the rump session of LICS 2003].
	www.haverford.edu /cmsc/slindell (1024 words)

	Le séminaire du LSV -- Alexander Rabinovich (Tel Aviv University) - Jeudi 20 avril 2000 (Site not responding. Last check: 2007-11-07)
		Temporal Logic as means of arguing about programs came to focus in the seminal work of Pnueli and became a major topic of research.
		It was clear that the convenient and succinct way to argue about time was and remained Monadic Logic of order (ML), and that temporal logic was just a way to rephrase an important set of formulas in Monadic Logic.
		An extension of the logic had to be found which nonetheless was not expressive enough to make it undecidable.
	www.lsv.ens-cachan.fr /Seminaires/OLDSEM/LS_m6.html (237 words)

	Dynamic Logic DigitalLink
		DigitalLink™, a unique research offering from Dynamic Logic and Millward Brown, is a copy testing solution for online advertising that provides advertisers, agencies and publishers with consumer feedback on their creative executions before the campaign goes live.
		Respondents are recruited either from a panel or via the Web and are exposed to a single creative unit in a lab environment.
		This monadic research design, using forced exposure, eliminates typically observed biases from media placement as well as the order in which ads are tested.
	www.dynamiclogic.com /na/products/DigitalLink (385 words)

	DBLP: Bruno Courcelle
		Bruno Courcelle, Sang-il Oum: Vertex-minors, monadic second-order logic, and a conjecture by Seese.
		Bruno Courcelle: Monadic Second-Order Logic and Hypergraph Orientation LICS 1993: 179-190
		Bruno Courcelle: Monadic Second-Order Logic and Context-Free Graph-Grammars.
	www.informatik.uni-trier.de /~ley/db/indices/a-tree/c/Courcelle:Bruno.html (1631 words)

	Monadic Chain Logic Over Iterations and Applications to Pushdown Systems (Site not responding. Last check: 2007-11-07)
		Logical properties of iterations of relational structures are studied and these decidability results are applied to the model checking of a powerful extension of pushdown systems.
		It is shown that the monadic chain theory of the iteration of a structure A (in the sense of Shelah and Stupp) is decidable in case the first-order theory of the structure A is decidable.
		This result follows from our decidability result for the monadic chain theory of the iteration.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/lics/2006/2631/00/2631toc.xml&DOI=10.1109/LICS.2006.35 (239 words)

	WoLLIC'2001 - Title and Abstract of Tutorial Lectures
		Second, because the verification of a property expressed in Monadic Second-Order Logic can be done in linear time on certain graphs constructed in an appropriate hierarchical way (for an example, the graphs of tree-width at most $k$).
		These interesting algorithmic and grammatical properties are based on the equivalence between monadic second-order logic and finite automata on finite trees (i.e., trees that represent finite well-formed terms written over a finite set of operation symbols).
		Usual linear logic, which uses a modal operator to control contraction and weakening, is now able to represent programs through formalizations which begin to look like real programming languages and can speak adequately about many of their properties.
	www.di.ufpe.br /~wollic/wollic2001/tutorials.html (2105 words)

	Category:Mathematical logic - Wikipedia, the free encyclopedia
		Mathematical logic is considered by many to be synonymous with symbolic or formal logic.
		However, it is also be described as the branch of formal logic that investigates the logical foundations of mathematics.
		This page was last modified 12:17, 26 July 2005.
	en.wikipedia.org /wiki/Category:Mathematical_logic (59 words)

	Papers by Ron Fagin
		On monadic NP vs. monadic co-NP, with Larry Stockmeyer and Moshe Vardi.
		An internal semantics for modal logic, with Moshe Y. Vardi.
		An equivalence between relational database dependencies and a fragment of propositional logic, with Yehoshua Sagiv, Claude Delobel, and D. Stott Parker, Jr.
	www.almaden.ibm.com /cs/people/fagin/papers.html (4688 words)

	Monadic Second-Order Logic-10;abstract
		Section 4 shows that every graph property that is expressible in MS logic with help of an auxiliary "invariant" linear order on the vertices is recognizable.
		This extension of MS logic is our most expressive candidate for logical characterizations of recognizable sets of graphs.
		We obtain logical characterizations of recognizable sets of cographs and of graphs having modular decompositions with prime graphs of bounded size.
	www.labri.u-bordeaux.fr /Perso/~courcell/Art10.html (1330 words)

	Abstract of a paper to be presented at MFCS'99 (Site not responding. Last check: 2007-11-07)
		On the structure of the monadic logic of the binary tree
		Since the work of Rabin (Rabin 1969), it has been known that any monadic second order formula (MS-formula) over the binary tree with successor functions is equivalent to a monadic Sigma_3 formula.
		In this paper, we show this upper bound is optimal in the sense that there is a monadic Sigma_2 formula, stating the existence of a path where a given predicate p holds infinitely often, which is not equivalent to any Pi_2 formula.
	www.tcs.uni.wroc.pl /mfcs99/abstract.phtml?paper_id=W107 (161 words)

	Henzinger/Raskin/Schobbens: The Regular Real-Time Languages (Site not responding. Last check: 2007-11-07)
		The counter-free omega-regular languages are definable by temporal logic, or equivalently, by the first-order fragment of the Sequential Calculus.
		First, we show that temporal logic with event clocks defines the same class of timed omega-languages as temporal logic with nonsingular time bounds, and we identify a first-order monadic theory that also defines this class.
		By contrast, the first two classes are definable by fully decidable formalisms from temporal logic, from automata theory, and from monadic logic.
	www-cad.eecs.berkeley.edu /~tah/Publications/the_regular_real-time_languages.html (453 words)

	Literature (Site not responding. Last check: 2007-11-07)
		We investigate this in both algebraic and logical contexts where equality is defined by an equational theory and more generally by a definitive clause equality theory E. We show how E-disunification can be reduced to E-unification, that is, solving equations only, and give a disunification algorithm for theories given a unification algorithm.
		This logic is as expressive as the alternation-free fragment of the modal mu-calculus identified by Emerson and Lei, and it may therefore be used to encode a number of temporal logics and behavioral preorders.
		The conclusion is drawn that temporal logic, construed correctly, provides a vehicle for a large range of problem domains that have previously been inaccessible to pure logic programmers.
	www-i2.informatik.rwth-aachen.de /leucker/Literatur/lit.html (6371 words)

	Monadic Encyclopedia Article, History, Biography @ Local Color Art (Site not responding. Last check: 2007-11-07)
		Find monadic - Your relevant result is a click away!
		Of, pertaining to, or like, a monad, in any of its senses.
		monadic - unary, when describing an operator or function.
	www.alienartifacts.com /search/encyclopedia/Monadic (215 words)

	SYBOLIC PROCESSING IN PASCAL - Chapter 19
		Whereas the monadic logic system determined whether a formula is a logical truth (or true in all interpretations), this system determines whether a formula is true in a particular interpretation.
		For finite interpretations, but only for finite interpretations, a universally quantified formula is logically equivalent to a conjunction, an existentially quantified formula is logically equivalent to a disjunction.
		The conjuncts or disjuncts have to be substitution instances of the given formula in which all occurrences of the variable that are bound by the quantifier are replaced by a reference to an individual in the domain.
	www.latrobe.edu.au /philosophy/phimvt/sympas/s43datbas.html (10036 words)

	FI Abstracts vol. 62
		The choice of the temporal logic became an arbitrary decision which was no longer backed up by the expressive power of classical logic.
		First as extensions of temporal logic, ignoring the framework of classical predicate logic, and then, with the authors' work, within the framework of monadic logic of order.
		To choose such a logic we pursue two goals: first, to make formalization of verification problems rather direct, without unjustified simplifications, and second, to have a logic which permits to describe decidable classes of the verifications problem covering the particular problems we are interested in.
	fi.mimuw.edu.pl /abs62.html (3481 words)

	Sequentiality, Second Order Monadic Logic and Tree Automata (Site not responding. Last check: 2007-11-07)
		We show here that the sequentiality of P is definable in SkS, the second-order monadic logic with k successors, provided P is definable in SkS.
		We derive several known and new consequences of this remark: 1-- strong sequentiality, as defined by Huet and Lévy, of a left linear (possibly overlapping) rewrite system is decidable, 2-- NV-sequentiality, as defined by Oyamaguchi, is decidable, even in the case of overlapping rewrite systems 3-- Sequentiality of any linear shallow rewrite system is decidable.
		Then we describe a direct construction of a tree automaton recognizing the set of terms that do have needed redexes, which, again, yields immediate consequences: 1-- Strong sequentiality of possibly overlapping linear rewrite systems is decidable in EXPTIME, 2-- For strongly sequential rewrite systems, needed redexes can be read directly on the automaton.
	www.lsv.ens-cachan.fr /~comon/comon95licsa.html (220 words)

	PlanetMath: generalized quantifier (Site not responding. Last check: 2007-11-07)
		In general, the monadic quantifiers are those of type
		(Mathematical logic and foundations :: General logic :: Higher-order logic and type theory)
		(Mathematical logic and foundations :: Model theory :: Logic with extra quantifiers and operators)
	planetmath.org /encyclopedia/Monadic.html (184 words)

	Publications de B. Courcelle (1987-1996)
		[MSG4] The monadic second-order logic of graphs IV, Definability properties of equational graphs, Annals Pure Applied Logic 49 (1990) 193-255 (presented at ICALP 1989, Stresa, Italy).
		[MSG5] The monadic second-order logic of graphs V : On closing the gap between definability and recognizability, Theor.
		[GT2] Graph grammars, monadic second-order logic and the theory of graph minors, in "Graph Structure Theory", N. Robertson et P. Seymour eds., Contemporary Mathematics (Amer.
	www.labri.fr /Perso/~courcell/Publications87-96.html (750 words)

	Attribute Grammars and Monadic Second Order Logic (Site not responding. Last check: 2007-11-07)
		It is shown that formulas in monadic second order logic (MSO) with one free variable can be mimicked by attribute grammars with a designated boolean attribute and vice versa.
		We prove that MSO formulas with two free variables have the same power in defining binary relations on nodes of a tree as regular path languages have.
		Last, it is proven that MSO tree transducers have the same strength as attributed tree transducers with the single use requirement and flags.
	www.liacs.nl /MScThesis/IR96-15.html (129 words)

	FREIDOK - System verification tools based on Monadic Logics
		These logics are amongst the most expressive logics that are known to be decidable.
		These logics suffer, however, from two drawbacks that strongly limit their application, namely the low-level language they provide to specify systems and properties, and the demanding computational complexity of their decision procedures.
		To this end, we first improve the existing approaches (i) by formalizing a new specification language which is expressive, intuitive and more user-friendly, and (ii) by providing a handle on the complexity of the logics' decision procedures.
	www.freidok.uni-freiburg.de /volltexte/1234 (599 words)

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