construction of response solutions for two classes of quasi periodically forced four dimensional nonlinear systems with degenerate equilibrium point under small perturbations abstract by developing two kam theorems in this paper we show that two classes of quasi periodically forced four dimensional nonlinear systems with degenerate equilibrium point a reversible system and a non conservative system admit a response solution under small perturbations for the degenerate reversible system applying special structure of unperturbed nonlinear term and herman method we successfully control the shift of equilibrium point which is difficult in view of the degenerate linear term for the degenerate non conservative system kam method is brought into force even in completely degenerate case because of the restrictions on the smallness and average of perturbation moreover arithmetic condition on the frequency is assumed to satisfy the brjuno russmann s non resonant condition by the poschel russmann kam method we prove that these two kinds of perturbed systems can be reduced to a suitable normal form with zero as equilibrium point by a quasi periodic transformation

reasoning with the finitely many valued łukasiewicz fuzzy description logic sroiq fuzzy description logics are a formalism for the representation of structured knowledge affected by imprecision or vagueness they have become popular as a language for fuzzy ontology representation to date most of the work in this direction has focused on the so called zadeh family of fuzzy operators or fuzzy logic which has several limitations in this paper we generalize existing proposals and show how to reason with a fuzzy extension of the logic sroiq the logic behind the language owl 2 under finitely many valued lukasiewicz fuzzy logic we show for the first time that it is decidable over a finite set of truth values by presenting a reasoning preserving procedure to obtain a non fuzzy representation for the logic this reduction makes it possible to reuse current representation languages as well as currently available reasoners for ontologies

satisfiability in many valued sentential logic is np complete abstract cook s np completeness theorem is extended to all many valued sentential logics including the infinite valued calculus of ukasiewicz

on similarity in fuzzy description logics this paper is a contribution to the study of similarity relations between objects represented as attribute value pairs in fuzzy description logics for this purpose we use concrete domains in the fuzzy description logic i a l c e f d associated either with a left continuous or with a finite t norm we propose to expand this fuzzy description logic by adding a similarity box sbox including axioms expressing properties of fuzzy equalities we also define a global similarity between objects from similarities between the values of each object attribute local similarities and we prove that the global similarity defined using a t norm inherits the usual properties of the local similarities reflexivity symmetry or transitivity we also prove a result relative to global similarities expressing that in the context of the logic mtl similar objects have similar properties being these properties expressed by predicate formulas evaluated in these objects

on the failure of the finite model property in some fuzzy description logics fuzzy description logics dls are a family of logics which allow the representation of and the reasoning with structured knowledge affected by vagueness although most of the not very expressive crisp dls such as alc enjoy the finite model property fmp this is not the case once we move into the fuzzy case in this paper we show that if we allow arbitrary knowledge bases then the fuzzy dls alc under lukasiewicz and product fuzzy logics do not verify the fmp even if we restrict to witnessed models in other words finite satisfiability and witnessed satisfiability are different for arbitrary knowledge bases the aim of this paper is to point out the failure of fmp because it affects several algorithms published in the literature for reasoning under fuzzy dls

on the relative expressiveness of description logics and predicate logics abstract it is natural to view concept and role definitions in description logics as expressing monadic and dyadic predicates in predicate calculus we show that the descriptions built using the constructors usually considered in the dl literature are characterized exactly as the predicates definable by formulas in tl3 the subset of first order predicate calculus with monadic and dyadic predicates which allows only three variable symbols in order to handle number bounds we allow numeric quantifiers and for transitive closure of roles we use infinitary disjunction using previous results in the literature concerning languages with limited numbers of variables we get as corollaries the existence of formulas of fopc which cannot be expressed as descriptions we also show that by omitting role composition descriptions express exactly the formulas in tl2 which is known to be decidable

fuzzy description logics with general t norms and datatypes fuzzy description logics dls are a family of logics which allow the representation of and the reasoning within structured knowledge affected by vagueness although a relatively important amount of work has been carried out in the last years current fuzzy dls still present several limitations in this work we face two problems the common restriction to zadeh and lukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets in particular we propose a semantics based on the use of a general left continuous t norm and an involutive negation specially focused on product logic and furthermore we show how to handle functional concrete roles relating individuals of the domain and strings real or integer numbers

the limits of decidability in fuzzy description logics with general concept inclusions fuzzy description logics dls can be used to represent and reason with vague knowledge this family of logical formalisms is very diverse each member being characterized by a specific choice of constructors axioms and triangular norms which are used to specify the semantics unfortunately it has recently been shown that the consistency problem in many fuzzy dls with general concept inclusion axioms is undecidable in this paper we present a proof framework that allows us to extend these results to cover large classes of fuzzy dls on the other hand we also provide matching decidability results for most of the remaining logics as a result we obtain a near universal classification of fuzzy dls according to the decidability of their consistency problem

weakly connected quasi periodic iscillators fm interactions and multiplexing in the brain we prove that weakly connected networks of quasi periodic multifrequency oscillators can be transformed into a phase model by a continuous change of variables the phase model has the same form as the one for periodic oscillators with the exception that each phase variable is a vector when the oscillators have mutually nonresonant frequency rotation vectors the phase model uncouples this implies that such oscillators do not interact even though there might be physical connections between them when the frequency vectors have mutual low order resonances the oscillators interact via phase deviations this mechanism resembles that of the fm radio with a shared feature multiplexing of signals possible applications to neuroscience are discussed

phase description of oscillatory convection with a spatially translational mode abstract we formulate a theory for the phase description of oscillatory convection in a cylindrical hele shaw cell that is laterally periodic this system possesses spatial translational symmetry in the lateral direction owing to the cylindrical shape as well as temporal translational symmetry oscillatory convection in this system is described by a limit torus solution that possesses two phase modes one is a spatial phase and the other is a temporal phase the spatial and temporal phases indicate the position and oscillation of the convection respectively the theory developed in this paper can be considered as a phase reduction method for limit torus solutions in infinite dimensional dynamical systems namely limit torus solutions to partial differential equations representing oscillatory convection with a spatially translational mode we derive the phase sensitivity functions for spatial and temporal phases these functions quantify the phase responses of the oscillatory convection to weak perturbations applied at each spatial point using the phase sensitivity functions we characterize the spatiotemporal phase responses of oscillatory convection to weak spatial stimuli and analyze the spatiotemporal phase synchronization between weakly coupled systems of oscillatory convection

reasoning within expressive fuzzy rough description logics it is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge based applications description logics dls are suitable well known logics for managing structured knowledge that have gained considerable attention the last decade the current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in dls are analyzed in this paper an integration between the theories of fuzzy dls and rough dls has been attempted by providing fuzzy rough dls based on fuzzy rough set theory the syntax semantics and properties of fuzzy rough dls are given it is proved that the satisfiability subsumption entailment and abox consistency reasoning in fuzzy rough dls may be reduced to the abox consistency reasoning in the corresponding fuzzy dls

triangular norm based predicate fuzzy logics the paper surveys the present state of knowledge on t norm based predicate fuzzy logics with their double semantics standard the set of truth values being the real interval 0 1 and general with abstract algebras of truth functions

multiple almost periodic solutions in nonautonomous delayed neural networks a general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed we consider a general class of nonautonomous neural networks with delays and various activation functions a geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed we further derive criteria under which the n neuron network admits 2n exponentially stable sets in addition we establish the existence of 2n exponentially stable almost periodic solutions for the system when the connection strengths time lags and external bias are almost periodic functions of time through applying the contraction mapping principle finally three numerical simulations are presented to illustrate our theory

on the un decidability of fuzzy description logics under łukasiewicz t norm recently there have been some unexpected results concerning fuzzy description logics fdls with general concept inclusions gcis they show that unlike the classical case the dl alc with gcis does not have the finite model property under lukasiewicz logic or product logic the proposed reasoning algorithms are neither correct nor complete and specifically knowledge base satisfiability is an undecidable problem for product logic in this work we show that knowledge base satisfiability is also an undecidable problem for lukasiewicz logic we additionally provide a decision algorithm for acyclic alc knowledge bases under lukasiewicz logic via a mixed integer linear programming milp based procedure note however that the decidability of this problem is already known while similar milp based algorithms have been proposed in the literature for acyclic alc knowledge bases under lukasiewicz logic none of them exhibit formal proofs of their correctness and completeness which is the additional contribution here

mniblos a smt based solver for continuous t norm based logics and some of their modal expansions in the literature little attention has been paid to the development of solvers for systems of mathematical fuzzy logic and in particular there are few works concerned with infinitely valued logics in this paper it is presented mniblos a modal nice bl logics solver a modular smt based solver complete with respect to a wide family of continuous t norm based fuzzy modal logics both with finite and infinite universes restricting the modal structures to the finite ones at the propositional level the solver works with some of the best known infinitely valued fuzzy logics including bl ukasiewicz godel and product logics and with all the continuous t norm based logics that can be finitely expressed in terms of the previous ones concerning the modal expansion mniblos imposes no boundary on the cardinality of the modal structures considered the solver allows to test 1 satisfiability of equations tautologicity and logical consequence problems the logical language supported extends the usual one of fuzzy modal logics with rational constants and the monteiro baaz operator the code of mniblos is of free distribution and can be found in the web page of the author

fuzzy sets and formal logics the paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics our focus is on the historical side of these developments

model checking fuzzy computation tree logic traditional temporal logics such as linear temporal logic and computation tree logic are widely used to specify properties of reactive systems model checking is a well established technique for verifying if a desired property described as a temporal logic formula holds over a reactive system model this paper presents fuzzy computation tree logic fctl a fuzzy extension of temporal logics by combining general fuzzy logic with computation tree logic and discusses its model checking problem first the notion of fuzzy kripke structures fkss and the syntax and semantics of their specification language fctl are introduced then we give a direct model checking algorithm for fctl over fks on the other hand we study when fctl model checking problem can be reduced to classical model checking ones and give a reduction method for an important fragment of fctl

relational compositions in fuzzy class theory we present a method for mass proofs of theorems of certain forms in a formal theory of fuzzy relations and classes the method is based on formal identification of fuzzy classes and inner truth values with certain fuzzy relations which allows transferring basic properties of sup t and inf r compositions to a family of more than 30 composition related operations including sup t and inf r images pre images cartesian products domains ranges resizes inclusion height plinth etc besides yielding a large number of theorems on fuzzy relations as simple corollaries of a few basic principles the method provides a systematization of the family of relational notions and generates a simple equational calculus for proving elementary identities between them thus trivializing a large part of the theory of fuzzy relations

three coupled oscillators mode locking global bifurcations and toroidal chaos abstract many systems exhibit behaviour which can be described by three coupled oscillators provided the coupling is not too strong such systems can be modelled by maps of the two torus to itself in this paper we describe and explain those aspects of the bifurcation diagram for two parameter families of torus maps that involve change of mode locking type we introduce the concepts of partial and full mode locking for the coupled oscillators these notions correspond to the presence of one or two rational relations between the frequencies respectively numerical investigation of a particular family of torus maps reveals an intricate web of global bifurcations in order to explain the results we first show that we can approximate maps in the neighbourhood of a rational translation to arbitrary order by the time 1 map of a flow on the torus then we analyse those condimension 1 and 2 bifurcations for flows on the torus which change the set of frequency ratios we find a large variety of bifurcation diagrams in particular many involving homotopically non trivial saddle connections next we ask how the picture changes when the time 1 maps of a family of flows are perturbed to a general family of diffeomorphisms we find toroidal chaos in the neighbourhood of all these bifurcations meaning that there exist orbits which perform a pseudo random sequence of rotations in different directions around the torus the corresponding behaviour for the coupled oscillators is that the frequency ratios perform a random walk finally we show how all these ingredients can be put together to give global scenarios for bifurcation for families of torus maps which we believe to be of general applicability to physical systems with three weakly coupled modes of oscillation

skolemization and herbrand theorems for lattice valued logics abstract skolemization and herbrand theorems are obtained for first order logics based on algebras with a complete lattice reduct and operations that are monotone or antitone in each argument these lattice valued logics defined as consequence relations on inequations between formulas typically lack properties underlying automated reasoning in classical first order logic such as prenexation deduction theorems or reductions from consequence to satisfiability skolemization and herbrand theorems for the logics therefore take various forms applying to the left or right of consequences and restricted classes of inequations in particular in the presence of certain witnessing conditions they admit sound parallel skolemization procedures where a strong quantifier is removed by introducing a finite disjunction or conjunction of formulas with new function symbols a general expansion lemma is also established that reduces consequence in a lattice valued logic between inequations containing only strong occurrences of quantifiers on the left and weak occurrences on the right to consequence between inequations in the corresponding propositional logic if propositional consequence is finitary this lemma yields a herbrand theorem for the logic

logical characterizations of regular equivalence in weighted social networks abstract social network analysis is a methodology used extensively in social science classical social networks can only represent the qualitative relationships between actors but weighted social networks can describe the degrees of connection between actors in a classical social network regular equivalence is used to capture the similarity between actors based on their links to other actors specifically two actors are deemed regularly equivalent if they are equally related to equivalent others the definition of regular equivalence has been extended to weighted social networks in two ways the first definition called regular similarity considers regular equivalence as an equivalence relation that commutes with the underlying graph edges while the second definition called generalized regular equivalence is based on the notion of role assignment or coloring a role assignment resp coloring is a mapping from the set of actors to a set of roles resp colors the mapping is regular if actors assigned to the same role have the same roles in their neighborhoods recently it was shown that social positions based on regular equivalence can be syntactically expressed as well formed formulas in a kind of modal logic thus actors occupying the same social position based on regular equivalence will satisfy the same set of modal formulas in this paper we present analogous results for regular similarity and generalized regular equivalence based on many valued modal logics

generalized fuzzy rough description logics description logics dls are a family of logics for representing structured knowledge which have proved to be very useful as ontology languages classical dls are not suitable to represent vague pieces of information the attempts to achieve a solution have led to the birth of fuzzy dls and rough dls in this work we provide a simple solution to join these two formalisms and define a fuzzy rough dl this logic is more general than other related approaches including tight and loose fuzzy rough approximations and being independent of the fuzzy logic operators considered we show the usefulness of our approach by presenting some uses case and we also describe how to extend two reasoning algorithms for fuzzy dls which are implemented in the fuzzy dl reasoners fuzzydl and delorean

lewis law versus feltham s law in soap froth abstract the scaling of area and perimeter of n sided cells versus n in a two dimensional cellular pattern are investigated lewis law states that a n is linear in n while feltham s law states that the perimeter e n is linear in n we have tested these two different predictions on soap froth for large samples starting with approximately 5000 cells at different times and different gap thicknesses we conclude that feltham s law has a smaller statistical error than lewis law we also compared the results with several two dimensional voronoi constructions of random points and perturbed triangular lattice we found that the error bars of the lewis s law and feltham s law are comparable in the voronoi constructions using geometric constraints we argue and verified by experimental data that there is a universal law obeyed by the slopes and intercepts of these laws on all samples

reasoning in fuzzy description logics using automata automata based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics and in particular in description logics dls very recently the ideas behind these automata based approaches were adapted for reasoning also in fuzzy extensions of dls with semantics based either on finitely many truth degrees or the godel t norm over the interval 0 1 clearly due to the different semantics in these logics the construction of the automata for fuzzy dls is more involved than for the classical case in this paper we provide an overview of the existing automata based methods for reasoning in fuzzy dls with a special emphasis on explaining the ideas and the requirements behind them the methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words overall we provide a comprehensive perspective on the automata based methods currently in use and the many complexity results obtained through them

making fuzzy description logic more general a version of fuzzy description logic based on the basic continuous t norm based fuzzy predicate logic bl is presented problems of satisfiability validity and subsumption of concepts are discussed and reduced to problems of fuzzy propositional logic known to be decidable for any continuous t norm for lukasiewicz t norm some stronger results are obtained

bisimulation and bisimilarity for fuzzy description logics under the godel semantics abstract description logics dls are a suitable formalism for representing knowledge about domains in which objects are described not only by attributes but also by binary relations between objects fuzzy extensions of dls can be used for such domains when data and knowledge about them are vague and imprecise one of the possible ways to specify classes of objects in such domains is to use concepts in fuzzy dls as dls are variants of modal logics indiscernibility in dls is characterized by bisimilarity the bisimilarity relation of an interpretation is the largest auto bisimulation of that interpretation in dls and their fuzzy extensions such equivalence relations can be used for concept learning in this paper we define and study fuzzy bisimulation and bisimilarity for fuzzy dls under the godel semantics as well as crisp bisimulation and strong bisimilarity for such logics extended with involutive negation the considered logics are fuzzy extensions of the dl alc r e g a variant of pdl with additional features among inverse roles nominals qualified or unqualified number restrictions the universal role local reflexivity of a role and involutive negation we formulate and prove results on invariance of concepts under fuzzy resp crisp bisimulation conditional invariance of fuzzy tboxes aboxes under bisimilarity resp strong bisimilarity and the hennessy milner property of fuzzy resp crisp bisimulation for fuzzy dls without resp with involutive negation under the godel semantics apart from these fundamental results we also provide results on using fuzzy bisimulation to separate the expressive powers of fuzzy dls as well as results on using strong bisimilarity to minimize fuzzy interpretations

collective synchronization of pulse coupled oscillators and excitable units abstract a phase model is proposed and studied for a population of integrate and fire type oscillators and excitable units with pulsatile coupling the units are subject to external noise and their mutual connection is all to all an evolution equation is derived for the phase distribution in a closed form its steady state analysis in the limit of weak noise shows the possibility of collective bistability the evolution equation is simplified drastically when the coupling as well as noise is sufficiently weak this reduction of equation enables analytical calculation of various quantities among others the stability of the steady distribution is analyzed explicity and the onset of collective oscillations is described in terms of the hopf bifurcation it is also shown that the present model is improved in some respects by introducing absolute refractoriness

global competition and local cooperation in a network of neural oscillators abstract an architecture of locally excitatory globally inhibitory oscillator networks is proposed and investigated both analytically and by computer simulation the model for each oscillator corresponds to a standard relaxation oscillator with two time scales oscillators are locally coupled by a scheme that resembles excitatory synaptic coupling and each oscillator also inhibits other oscillators through a common inhibitor oscillators are driven to be oscillatory by external stimulation the network exhibits a mechanism of selective gating whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern while preventing the other oscillators from jumping up we show analytically that with the selective gating mechanism the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks computer simulations demonstrate the model s promising ability for segmenting multiple input patterns in real time this model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure ground segregation

computational complexity of t norm based propositional fuzzy logics with rational truth constants if a continuous t norm on 0 1 maps pairs of rationals into rationals then the corresponding fuzzy propositional calculus can be extended by rational truth constants and bookkeeping axioms for them lukasiewicz t norm is the classical example computational complexity of such logics is studied consequences for fuzzy description logic are formulated

attributive concept descriptions with complements abstract we investigate the consequences of adding unions and complements to attributive concept descriptions employed in terminological knowledge representation languages it is shown that deciding coherence and subsumption of such descriptions are pspace complete problems that can be decided with linear space

fuzzy bisimulation for godel modal logic bisimulation is a central concept in the model theory of modal logic with extensive computational applications it is a relation between two models in which related states have identical atomic properties and matching transition possibilities bisimulation captures the expressive power of propositional modal logic in the sense that bisimilar states are not distinguishable by any propositional modal formula in recent years fuzzy modal logic has received much attention because of the connection between uncertainty measures and fuzzy modalities in this paper we define the notion of fuzzy bisimulation and prove that in a fuzzified version it bears the same relationship to fuzzy modal logic that bisimulation bears to propositional modal logic