minimal belief and negation as failure abstract fangzhen lin and yoav shoham defined a propositional nonmonotonic logic which uses two independent modal operators one of them represents minimal knowledge the other is related to the ideas of justification as understood in default logic and of negation as failure we describe a simplified version of that system show how quantifiers can be included in it and study its relation to circumscription and default logic to logic programming and to the theory of epistemic queries developed by hector levesque and ray reiter

some mean values related to the quasi arithmetic mean in this article we study new mean values and their properties related to the quasi arithmetic mean and their properties in the spirit of h haruki and th m rassias

on fixed points of multivalued functions on complete lattices and their application to generalized logic programs unlike monotone single valued functions multivalued mappings may have zero one or possibly infinitely many minimal fixed points the contribution of this work is twofold first we overview and investigate the existence and computation of minimal fixed points of multivalued mappings whose domain is a complete lattice and whose range is its power set second we show how these results are applied to a general form of logic programs where the truth space is a complete lattice we show that a multivalued operator can be defined whose fixed points are in one to one correspondence with the models of the logic program

generalized functional identities with anti automorphisms and derivations on prime rings i abstract the concept of a generalized functional identity gfi with anti automorphisms and derivations is a generalization of the notion of a generalized polynomial identity gpi with anti automorphisms and derivations in the present paper we show that either a prime ring is gpi or such gfis have only the obvious solutions our results simultaneously generalize the results of martindale rowen lanski kharchenko and chuang on gpis and a number of earlier results on gfis

on fuzzy modal logics s5 c the fuzzy variant s5 c of the well known modal logic s5 is studied c being a recursively axiomatized fuzzy propositional logic extending the basic fuzzy logic bl three kinds of kripke models are introduced and corresponding deductive systems are found

a logic of knowledge and justified assumptions abstract in this paper we define the logic gk of knowledge and justified assumptions gk is best understood as a formalization of autoepistemic reasoning processes that are more general than those in moore s autoepistemic logic and is formally defined via a modification of shoham s preference semantics we show that gk includes not only moore s autoepistemic logic but also reiter s default logic to our knowledge gk is the first complete semantic unification of the two logics similarly to circumscription gk is based on the notion of logical minimization and thus provides a bridge between circumscription and fixed point nonmonotonic logics an outstanding problem in nonmonotonic logics as an application of this bridge we propose a formalization of logic programs with negation as failure in circumscription

on herstein s lie map conjectures i first published in transactions american mathematical society in vol 353 no 10 pp 4235 4260 published by the american mathematical society

lie isomorphisms in prime rings with involution abstract let r and r be prime rings with involutions of the first kind and with respective lie subrings of skew elements k and k furthermore assume rc c 1 4 9 16 25 64 where c is the extended centroid of r it is shown that any lie isomorphism of k onto k can be extended uniquely to an associative isomorphism of k onto k where k and k are respectively the associative subrings generated by k and k

on herstein s lie map conjectures iii abstract in the two papers on herstein s lie map conjectures i and ii solutions of all of herstein s problems concerning lie isomorphisms and derivations were given under the assumption that the algebras involved were of sufficiently high dimension in the present paper we remove this restriction thereby solving herstein s problems in full generality

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

new characterizations of some mean values the purpose of this paper is to give new characterizations of some mean values of two positive real numbers the arithmetic geometric and harmonic means of two positive real numbers are the fundamentals of this paper

lie derivations of the skew elements of prime rings with involution abstract letrbe a prime ring with involution of the first kind and characteristic 2 3 letkdenote the skew elements ofr and letcdenote the extended centroid ofr assume that rc c 1 4 16 it is shown that any lie derivation ofkinto itself can be extended to an ordinary derivation of k counterexamples are given for the low dimension cases

herstein s lie theory revisited an associative ring r becomes a jordan ring r under x 0 y xy yx and a lie ring r under x y xy yx in case r has an involution i e an antiautomorphism of period 1 or 2 then the set of symmetric elements s s e r 1 s s is a jordan subring of r and the set of skew elements k ker 1 k k is a lie subring of rp in the early 1950s herstein initiated a study of the jordan and lie ideals of r s and k in case that r was a simple associative ring either without or with an involution in the ensuring years his work has been generalized in various directions on the one hand to the setting of prime and semiprime rings and on the other hand to invariance conditions other than that given by ideals besides herstein himself we mention lanski as having been a major force in this program their influence is certainly felt in the present paper we have taken the liberty of using various arguments without making specific mention from their papers notably 6 and s other important contributions in this area have also been made by baxter chacron erickson montgomery osborn streb and others part of our motivation in writing this paper is to obtain the lie ideal theory for semiprime rings with involution by a somewhat different approach from the self contained elementary very clever methods embodied in the original style of herstein let us describe very briefly the spirit of our approach for r a ring with involution and 1 any ideal i e an ideal invariant under in k k is always a lie ideal of k which we shall call a standard lie ideal of k a

on additive isomorphisms of prime rings preserving polynomials we study additive isomorphisms of prime rings preserving a multilinear polynomial of degree 2 our main theorem generalizes a number of results obtained for jordan n jordan lie and lie triple isomorphisms of prime rings

on some further extensions of the characterizations of mean values by h haruki and th m rassias abstract the purpose of this paper is to give a characterization of some mean values of two positive real numbers in a real valued function m a b the arithmetic harmonic and some other means of two positive real numbers are the fundamentals of this paper

centralizing maps in prime rings with involution abstract let r be a prime ring with involution of characteristic 2 with center z skew elements k and extended centroid c theorem suppose k k 0 and k k is an additive map such that x x z for all x k then unless r is an order in a 16 dimensional central simple algebra there exists c and an additive map k c such that x x x for all x k

some inequalities involving means and their converses using an idea of j sandor and v e s szabo an inequality of ky fan and its generalizations are proved we also establish some converses of these inequalities as consequences some well known inequalities are obtained

on the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent s rational beliefs on gradable propositions it has recently been shown that in the same way as autoepistemic logic generalizes answer set programming fuzzy autoepistemic logic generalizes fuzzy answer set programming as well besides being related to answer set programming autoepistemic logic is also closely related to several modal logics to investigate whether a similar relationship holds in a fuzzy logical setting we firstly generalize the main modal logics for belief to the setting of finitely valued ukasiewicz logic with truth constants k c and secondly we relate them with fuzzy autoepistemic logics moreover we show that the problem of satisfiability checking in these logics is np complete finally we generalize levesque s results on stable expansions belief sets and only knowing operators to our setting and provide a complete axiomatization for a logic of only knowing in the k c framework

fuzzy autoepistemic logic and its relation to fuzzy answer set programming autoepistemic logic is an important formalism for nonmonotonic reasoning it extends propositional logic by offering the ability to reason about an agent s lack of beliefs moreover it is well known to generalize the stable model semantics of answer set programming fuzzy logics on the other hand are multi valued logics which allow to model the intensity to which properties are satisfied we combine these ideas to a fuzzy autoepistemic logic which can be used to reason about one s beliefs in the degrees to which properties are satisfied we show that many properties from classical autoepistemic logic e g the equivalence between autoepistemic models and stable expansions remain valid under this generalization in this paper we consider a version of fuzzy answer set programming and show that its answer sets can be equivalently described as models in fuzzy autoepistemic logic we also define a fuzzy logic of minimal belief and negation as failure and use this as a tool to show that fuzzy autoepistemic logic generalizes fuzzy answer set programming

skew commutators and lie isomorphisms in real von neumann algebras in this paper we study skew elementsrkand their commutators in a real factorr and prove that ifrandsare real factors not of typei1andi2then derived lie algebras rk rk and sk sk are isomorphic if and only ifrandsare isomorphic

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

commuting traces of multiadditive mappings abstract letrbe a prime ring andmann additive mapping onrsuch that m x x x 0 for allx r if char r 0 or n then there exist mappings iofrinto the extended centroidcofrsuch that m x x i 0 n i x x n i for allx r if in addition ris not algebraic of bounded degree n then for eachithere exists ani additive mappingmiofriintocsuch that i x mi x x for allx r

on functional identities in prime rings with involution abstract let a be a prime ring with involution let s be the symmetric elements let k be the skew elements let q ml be the maximal left ring of quotients x 1 x m noncommuting variables and e i f j g k h l a m 1 q ml i j k l 1 2 m we study functional identities of the form m i 1 e i i x i m j 1 x j f j j m k 1 g k k x k m l 1 x l h l l 0 for all x 1 x m a where e i i means e i x 1 x i x m etc in case s k is not algebraic of bounded degree 2 m definitive results are obtained as an application k commuting traces of symmetric n additive maps of either s or k into q ml are characterized

the zelmanov approach to jordan homomorphisms of associative algebras abstract zelmanov s work on prime jordan algebras leads to an idempotent free version of martindale s theorem on the extension of jordan homomorphisms and derivations from the hermitian elements h r of an associative algebra of degree 2 with involution to associative homomorphisms and derivations on r the condition that j h r be of degree 2 is replaced by the intrinsic condition that j z j h a consist entirely of values of zelmanov polynomials