wave operators and analytic solutions for systems of non linear klein gordon equations and of non linear schrodinger equations we consider in a 1 3 space time arbitrary finite systems of nonlinear klein gordon equations respectively schrodinger equations with an arbitrary local and analytic non linearity in the unknown and its first and second order space time respectively first order space derivatives having no constant or linear terms no restriction is given on the frequency sign of the initial data in the case of non linear klein gordon equations all masses are supposed to be different from zero

analytic smoothing effect for nonlinear schrodinger equation with quintic nonlinearity abstract we prove the global existence of analytic solutions to nonlinear schrodinger equation with quintic nonlinearity in n space dimensions for sufficiently small cauchy data with exponential decay the smallness assumption on the data is imposed in terms of the critical sobolev space h n 2 1 2 moreover a characterization of some class of analytic functions is given

an extension of pointwise circumscription abstract in this paper we generalize lifschitz s pointwise circumscription ander the first order framework the generalized version has the ability for simultaneously minimizing several predicates at finitely many pinpoints in a pointwise manner we show that if an anderlying first order theory is almost existential then the extended pointwise circumscription is complete with respect to minimal model semantics almost existential formulas are in the dual form of almost universal formulas which was proposed by lifschitz to investigate the satisfiability of circumscription this completeness result is a generalization of the result by kolaitis and papadimitriou who regarded the case of existential formulas we also give a partial answer to the question for exponential growth of the size of first order formulas equivalent to circumscription moreover we clarify that lifschitz s pointwise circumscription is complete in a slightly wider class of positive formulas

on solutions of the initial value problem for the nonlinear schrodinger equations on considere le probleme aux valeurs initiales pour l equation de schrodinger non lineaire de la forme iu t u f u 2 u t x r r n u 0 x x x r n on etudie la regularite des solutions quand les fonctions initiales ne sont pas regulieres

complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions we present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions this extends some known results due to s l qiu and m vuorinen

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

the suprem architecture a new intelligent paradigm abstract we investigate the model theory of the notion of circumscription and find completeness theorems that provide a partial converse to a result of mccarthy we show that the circumscriptive theorems are precisely the truths of the minimal models in the case of various classes of theories and for various versions of circumscription we also present an example of commonsense reasoning in which first order circumscription does not achieve the intuitive and desired minimization

an incremental algorithm for generating all minimal models the task of generating minimal models of a knowledge base is at the computational heart of diagnosis systems like truth maintenance systems and of nonmonotonic systems like autoepistemic logic default logic and disjunctive logic programs unfortunately it is np hard in this paper we present a hierarchy of classes of knowledge bases 1 2 with the following properties first 1 is the class of all horn knowledge bases second if a knowledge base t is in k then t has at most k minimal models and all of them may be found in time o lk2 where l is the length of the knowledge base third for an arbitrary knowledge base t we can find the minimum k such that t belongs to k in time polynomial in the size of t and last where k is the class of all knowledge bases it is the case that i 1 i k that is every knowledge base belongs to some class in the hierarchy the algorithm is incremental that is it is capable of generating one model at a time

existential second order logic over strings existential second order logic eso and monadic second order logic mso have attracted much interest in logic and computer science eso is a much expressive logic over successor structures than mso however little was known about the relationship between msoand syntatic fragments of eso we shed light on this issue by completely characterizing this relationship for the prefix classes of eso over strings i e finite successor structures moreover we determine the complexity of model checking over strings for all eso prefix classes let eso q denote the prefix class containing all sentences of the shape r q 4 where r is a list of predicate variables q is a first order predicate qualifier from the prefix set q and 4 is quantifier free we show that eso and eso are the maximal standard eso prefix classes contained in mso thus expressing only regular languages we further prove the following dichotomy theorem an eso prefix class either expresses only regular languages and is thus in mso or it expresses some np complete languages we also give a precise characterization of those eso prefix classes that are equivalent to mso over strings and of the eso prefix classes which are closed under complementation on strings

propositional circumscription and extended closed world reasoning are p p 2 complete abstract circumscription and the closed world assumption with its variants are well known nonmonotonic techniques for reasoning with incomplete knowledge their complexity in the propositional case has been studied in detail for fragments of propositional logic one open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is p 2 complete i e complete for a class of the second level of the polynomial hierarchy we answer this question by proving these problems p 2 complete and we show how this result applies to other variants of closed world reasoning

analyticity and global existence of small solutions to some nonlinear schrodinger equations in this paper we will study the nonlinear schrodinger equations begin gathered i partial t u tfrac 1 2 delta u left u right 2 u t x in mathbb r times mathbb r x n hfill u 0 x phi x x in mathbb r x n hfill end gathered it is shown that the solutions of exist and are analytic in space variables fort 0 if x h2n 1 2 xn decay exponentially as x andn 2

on the satisfiability of circumscription abstract etherington mercer and reiter showed on the basis of ideas of bossu and siegel that circumscription cannot lead to inconsistency for universal formulas we extend this result in three directions to formulas of a more general syntactic form to circumscription with some predicate symbols allowed to vary and to prioritized circumscription

analytic smoothing effect for global solutions to nonlinear schrodinger equations abstract we prove the global existence of analytic solutions to the cauchy problem for the cubic schrodinger equation in space dimension n 3 for sufficiently small data with exponential decay at infinity minimal regularity assumption regarding scaling invariance is imposed on the cauchy data

reasoning with minimal models efficient algorithms and applications reasoning with minimal models is at the heart of many knowledge representation systems yet it turns out that this task is formidable even when very simple theories are considered in this paper we introduce the elimination algorithm which performs in linear time minimal model finding and minimal model checking for a significant subclass of positive cnf theories which we call positive head cycle free hcf theories we also prove that the task of minimal entailment is easier for positive hcf theories than it is for the class of all positive cnf theories finally we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way

some computational aspects of circumscription the effects of circumscribing first order formulas are explored from a computational standpoint first extending work of v lifschitz it is shown that the circumscription of any existential first order formula is equivalent to a first order formula after this it is established that a set of universal horn clauses has a first order circumscription if and only if it is bounded when considered as a logic program thus it is undecidable to tell whether such formulas have first order circumscription finally it is shown that there arefirst order formulas whode circumscription has a conp complete model checking problem

nonlinear schrodinger equations in the sobolev space of critical order the cauchy problem for the nonlinear schrodinger equations is considered in the sobolev spacehn 2 rn of critical ordern 2 where the embedding intol rn breaks down and any power behavior of interaction works as a subcritical nonlinearity under the interaction of exponential type the existence and uniqueness is proved for globalhn 2 solutions with small cauchy data

on compact representations of propositional circumscription we prove that unless the polynomial hierarchy collapses at the second level the size of a purely propositional representation of the circumscription circ t of a propositional formula t grows faster than any polynomial as the size of t increases we then analyze the significance of this result in the related field of closed world reasoning

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

remarks on analytic smoothing effect for the schrodinger equation we study analytic smoothing effect of solutions to the schrodinger equation with cauchy data decaying exponentially at infinity the domain of analyticity in the space variables of solutions is described under weight conditions on the data in terms of the corresponding supporting function the domain of analyticity in the time variable is characterized by means of weight conditions of gaussian type on the data a generalization of various isometrical identities related to the analytic smoothing effect is introduced

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

saturation nonmonotonic reasoning and the closed world assumption abstract to deal with the problem of implicit negative information in databases it is necessary to use a nonmonotonic form of reasoning the form of reasoning described in this paper uses an ordering relation on interpretations of the type i is inferior to j if every elementary fact true in i is true in j in simple cases this rule may be defined by a set p of formulas implies a formula q if every minimal model of p satisfies q in more general cases this definition leads to paradox if p is consistent and has no minimal model p must not imply q and its negation we have 1 1 carefully formulated the definition of a special type of implication called sub implication to avoid this type of paradox 2 2 proved that if p is a set of clauses then p has a minimal model and more generally that every model of a set of clauses is minored by one of its minimal models 3 3 developed in this last case subject to certain conditions such as the use of a particular set of clauses called groundable clauses or g clauses a decidable algorithm to compute whether p implies q q being practically any formula

global existence of small analytic solutions to nonlinear schrodinger equations in this paper we consider the following nonlinear schrodinger equation in r n n 2 i u 1 2 u f u u u t x er r n u 0 x x xer n

on the tractability of minimal model computation for some cnf theories designing algorithms capable of efficiently constructing minimal models of conjunctive normal form theories cnfs is an important task in ai this paper provides new results along this research line and presents new algorithms for performing minimal model finding and checking over positive propositional cnfs and model minimization over propositional cnfs a cnf is positive if each of its clauses has at least a positive literal an algorithmic schema called the generalized elimination algorithm gea is presented that computes a minimal model of any positive cnf the schema generalizes the elimination algorithm ea 5 which computes a minimal model of positive head cycle free hcf cnf theories while the ea always runs in polynomial time in the size of the input hcf cnf the complexity of the gea depends on the complexity of the specific eliminating operator invoked therein which may in general turn out to be exponential therefore a specific eliminating operator is defined by which the gea computes in polynomial time a minimal model for a class of cnf that strictly includes head elementary set free hef cnf theories 14 which form in their turn a strict superset of hcf theories furthermore in order to deal with the high complexity associated with recognizing hef theories an incomplete variant of the gea called igea is proposed the resulting schema once instantiated with an appropriate elimination operator always constructs a model of the input cnf which is guaranteed to be minimal if the input theory is hef in the light of the above results the main contribution of this work is the enlargement of the tractability frontier for the minimal model finding and checking and the model minimization problems