value minimization in circumscription abstract minimization in circumscription has focussed on minimizing the extent of a set of predicates with or without priorities among them or of a formula although functions and other constants may be left varying during circumscription no earlier formalism to the best of our knowledge minimized functions in this paper we introduce and motivate the notion of value minimizing a function in circumscription intuitively value minimizing a function consists in choosing those models where the value of the function is minimal relative to an ordering on its range we first give the formulation of value minimization of a single function based on a syntactic transformation and then give a formulation in model theoretic terms we then discuss value minimization of a set of functions with and without priorities we show how lifschitz s nested abnormality theories can be used to express value minimization and discuss the prospect of its use for knowledge representation particularly in formalizing reasoning about actions

generalized van der waerden identities the idea of generalized van der waerden identities is introduced to facilitate the polynomial expansion of multi spin functions of the type that are frequently encountered in theoretical studies of ising spin systems

on relativized exponential and probabilistic complexity classes an oracle x is constructed such that the exponential complexity class ep x 2 equals the probabilistic class r r x this shows that it will be difficult to prove that ep 2 is different from r r although it seems very unlikely that these two classes are equal the result subsumes several known results about relativized computations i the existence of relativized polynomial hierarchies extending two levels long t 1978 dissertation purdue univ lafayette ind heller h 1984 a siam j comput 13 717 725 heller h 1984 b math systems theory 17 71 84 ii the existence of an oracle x such that bpp x p x 2 stockmeyer l 1983 proc 15th stoc pp 118 126 iii the existence of an oracle x such that np x is polynomially turing reducible to a sparse set wilson c 1983 proc 24th focs pp 329 334 immerman n and mahaney s 1983 conference on computational complexity theory santa barbara march 21 25 the result shows possible inclusion relations for nonrelativized complexity classes and points out that certain results about probabilistic complexity classes and about polynomial size circuits cannot be improved unless methods are applied which do not relativize

pp is as hard as the polynomial time hierarchy in this paper two interesting complexity classes pp and oplus text p are compared with ph the polynomial time hierarchy it is shown that every set in ph is polynomial time turing reducible to a set in pp and ph is included in text bp cdot oplus text p as a consequence of the results it follows that text pp subseteq text ph or oplus text p subseteq text ph implies a collapse of ph a stronger result is also shown every set in pp ph is polynomial time turing reducible to a set in pp

the spin 3 2 blume emery griffiths model abstract the spin 3 2 blume emery griffiths model is studied using the effective field theory based on the use of a probability distribution that correctly accounts for the single site kinematic relations the phase diagrams of the model on a square lattice are obtained

statistical mechanics of the spin 3 2 blume capel model on the bethe lattice using the recursion method abstract exact expressions for the magnetization or the dipole moment the quadrupolar moment and the curie temperature of the spin 3 2 blume capel model on the bethe lattice are derived using the recursion method the thermal variations of the magnetization and quadrupolar moment order parameters are studied in depth for a range of the coupling parameter d j and a number of characteristic behaviors for their thermal variations are obtained besides the stable branches of the order parameters we find the unstable branches of them which occur at low temperatures and near the first and second order phase transition temperatures finally the phase diagram and the critical behavior of the model are discussed

note about cardinality based circumscription abstract in a very interesting paper liberatore and schaerf showed how to express the leading proposals of belief revision using a circumscription in order to deal with one of the belief revision theories they had to introduce a new circumscription based on the cardinality instead of the classical set inclusion we give a few properties of this new circumscription in doing so we prove that in the finite case there is inter definability between ordinary circumscription and cardinality based circumscription we show why a technical result published in the initial paper cannot be true and we give a related result which is true instead where the respective roles of the varying or fixed propositions are reversed this result could help automatic computation we use the logical properties of circumscriptions and cardinality based circumscriptions in order to highlight the behavior of cardinality based circumscription and the importance of the fixed propositions this study allows a full description of the expressive power of cardinality based circumscription in the finite case and it provides some limitations in the infinite case

defeasible reasoning with variable degrees of justification the question addressed in this paper is how the degree of justification of a belief is determined a conclusion may be supported by several different arguments the arguments typically being defeasible and there may also be arguments of varying strengths for defeaters for some of the supporting arguments what is sought is a way of computing the on sum degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all relevant reasons i have in the past defended various principles pertaining to this problem in this paper i reaffirm some of those principles but propose a significantly different final analysis specifically i endorse the weakest link principle for the computation of argument strengths according to this principle the degree of justification an argument confers on its conclusion in the absence of other relevant arguments is the minimum of the degrees of justification of its premises and the strengths of the reasons employed in the argument i reaffirm my earlier rejection of the accrual of reasons according to which two arguments for a conclusion can result in a higher degree of justification than either argument by itself this paper diverges from my earlier theory mainly in its treatment of defeaters first it argues that defeaters that are too weak to defeat an inference outright may still diminish the strength of the conclusion second in the past i have also denied that multiple defeaters can result in the defeat of an argument that is not defeated by any of the defeaters individually in this paper i urge that there are compelling examples that support a limited version of this collaborative defeat the need to accommodate diminishers and collaborative defeat has important consequences for the computation of degrees of justification the paper proposes a characterization of degrees of justification that captures the various principles endorsed and constructs an algorithm for computing them

making the right exceptions this paper is about the logical properties of sentences of the form s s are normally p and starts from the idea that any logical theory for such sentences should meet the following simple requirement if the only available information about some object x is that x has property s it must be valid to infer by default that x has all the properties p that objects with property s normally have we investigate how this requirement can be met by theories developed within the framework of circumscription and specify a constraint the exemption principle that must be satisfied to do so this principle determines in cases of conflicting default rules which objects are exempted from which rules and as such is the main source for the capricious logical behavior of the sentences we are interested in to facilitate comparison and implementation we supply an algorithm for inheritance networks and prove that arguments that can be expressed in both frameworks are valid on the circumscriptive account if and only if the inheritance algorithm has a positive outcome

hyper polynomial hierarchies and the polynomial jump abstract assuming that the polynomial hierarchy ph does not collapse we show the existence of ascending sequences of ptime turing degrees of length 1 ck in pspace such that successors are polynomial jumps of their predecessors moreover these ptime degrees are all uniformly hard for ph this is analogous to the hyperarithmetic hierarchy which is defined similarly but with the computable turing degrees the lack of uniform least upper bounds for ascending sequences of ptime degrees causes the limit levels of our hyper polynomial hierarchy to be inherently non canonical this problem is investigated in depth and various possible structures for hyper polynomial hierarchies are explicated as are properties of the polynomial jump operator on the languages which are in pspace but not in ph

conditional entailment bridging two approaches to default reasoning abstract in recent years two conceptually different interpretations of default expressions have been advanced extensional interpretations in which defaults are regarded as prescriptions for extending one s set of beliefs and conditional interpretations in which defaults are regarded as beliefs whose validity is bound to a particular context the two interpretations possess virtues and limitations that are practically orthogonal to each other the conditional interpretations successfully resolve arguments of different specificity e g penguins don t fly in spite of being birds but fail to capture arguments of irrelevance e g concluding red birds fly from birds fly the opposite is true for the extensional interpretations this paper develops a new account of defaults called conditional entailment which combines the benefits of the two interpretations like prioritized circumscriptions conditional entailment resolves arguments by enforcing priorities among defaults however instead of having to be specified by the user these priorities are extracted automatically from the knowledge base similarly conditional entailment possesses a sound and complete proof theory based on interacting arguments and amenable to implementation in conventional atmss

evaluating the effect of semi normality on the expressiveness of defaults normal default logic ndl and semi normal default logic sndl are syntactically restricted variants of reiter s default logic dl although semi normal defaults have only a slightly more general form than normal defaults sndl does not share the nice properties of ndl e g semi monotonicity in this note we address the effect of semi normality on the expressive power of defaults using a classification method based on polynomial faithful and modular pfm translation functions the resulting classification indicates that sndl and dl are of equal expressive power which strictly exceeds that of ndl this strengthens an earlier result achieved by marek and truszczynski who establish the equivalence of weak semi normal defaults with general defaults furthermore it is established that prerequisite free fragments of dl and sndl pdl and psndl are of equal expressive power consequently psndl is less expressive than dl and sndl incomparable with ndl and more expressive than preferential entailment a generalized form of circumscription the latter result is in sharp contrast with imielinski s result which states that prerequisite free and semi normal default theories can be modularly translated into preferential entailment

on the relative complexity of hard problems for complexity classes without complete problems abstract we show that any recursive sequence of recursive sets which is ascending with respect to the standard polynomial time reducibility notions has no minimal upper bound as a consequence any complexity class with certain natural closure properties possesses either complete problems or no easiest hard problems a further corollary is that assuming p np the partial ordering of the polynomial time degrees of np sets is not complete and that there are no degree invariant approximations to np complete problems

on first order conditional logics abstract conditional logics have been developed as a basis from which to investigate logical properties of weak conditionals representing for example counterfactual and default assertions this work has largely centred on propositional approaches however it is clear that for a full account a first order logic is required existing or obvious approaches to first order conditional logics are inadequate in particular various representational issues in default reasoning are not addressed by extant approaches further these problems are not unique to conditional logic but arise in other nonmonotonic reasoning formalisms i argue that an adequate first order approach to conditional logic must admit domains that vary across possible worlds as well the most natural expression of the conditional operator binds variables although this binding may be eliminated by definition a possible worlds approach based on kripke structures is developed and it is shown that this approach resolves various problems that arise in a first order setting including specificity arising from nested quantifiers in a formula and an analogue of the lottery paradox that arises in reasoning about default properties

a decidable fragment of predicate calculus abstract we describe a decision procedure for what we call direct predicate calculus this fragment of predicate logic coincides with those formulas that can be proved in the gentzen sequent calculus with the rule of contraction eliminated it arose by thinking about what kinds of inferences should be considered obvious and in that sense characterizes fragments of logic by the tools available for proving results rather than by syntactic properties of formulas

results on translating defaults to circumscription abstract in this paper we define different concepts of translating a set of defaults into circumscription the most important of these modular translation requires that additive changes of specific facts not defaults of default theory translate to additive changes of the simple abnormality theory corresponding to circumscription we show that surprisingly enough an important class of defaults normal defaults with prerequisites does not have such a modular translation into circumscription abnormality theory we also establish the classes of defaults which are translatable into circumscription

modeling a dynamic and uncertain world i symbolic and probabilistic reasoning about change abstract intelligent agency requires some ability to predict the future an agent must ask itself what is presently its best course of action given what it now knows about what the world will be like when it intends to act this paper presents a system that uses a probabilistic model to reason about the effects of an agent s proposed actions on a dynamic and uncertain world computing the probability that relevant propositions will hold at a specified point in time the model allows for incomplete information about the world the occurrence of exogenous unplanned events unreliable sensors and the possibility of an imperfect causal theory the system provides an application program with answers to questions of the form is the probability that will hold in the world at time t greater than it is unique among algorithms for probabilistic temporal reasoning in that it tries to limit its inference according to the proposition time and probability threshold provided by the application the system will also notify the application if subsequent evidence invalidates its answer to a query

from answer set logic programming to circumscription via logic of gk we first embed pearce s equilibrium logic and ferraris s propositional general logic programs in lin and shoham s logic of gk a nonmonotonic modal logic that has been shown to include as special cases both reiter s default logic in the propositional case and moore s autoepistemic logic from this embedding we obtain a mapping from ferraris s propositional general logic programs to circumscription and show that this mapping can be used to check the strong equivalence between two propositional logic programs in classical logic we also show that ferraris s propositional general logic programs can be extended to the first order case and our mapping from ferraris s propositional general logic programs to circumscription can be extended to the first order case as well to provide a semantics for these first order general logic programs

nonmonotonic reasoning in the framework of situation calculus abstract most of the solutions proposed to the yale shooting problem have either introduced new nonmonotonic reasoning methods generally involving temporal priorities or completely reformulated the domain axioms to represent causality explicitly this paper presents a new solution based on the idea that since the abnormality predicate takes a situational argument it is important for the meanings of the situations to be held constant across the various models being compared this is accomplished by a simple change in circumscription policy when ab is circumscribed result rather than holds is allowed to vary in addition we need an axiom ensuring that every consistent situation is included in the domain of discourse ordinary circumscription will then produce the intuitively correct answer beyond its conceptual simplicity the solution proposed here has additional advantages over the previous approaches unlike the approach that uses temporal priorities it can support reasoning backward in time as well as forward and unlike the causal approach it can handle ramifications in a natural manner

computing circumscriptive databases i theory and algorithms abstract though circumscription was introduced by mccarthy over a decade ago there has been relatively little work on algorithms for computing circumscriptive databases in this paper we develop algorithms to compute the preferred models of circumscriptive databases at compile time using mixed integer linear programming techniques two advantages of this bottom up approach are that it makes efficient re use of previous computations and it provides much faster run time performance some other advantages of using linear programming to automate deduction at compile time are that its re optimization facilities elegantly accommodate database updates and also that it leads to a completely declarative formulation in which ordering of rules and literals in rule bodies plays no real role finally we plan to use a standard relational database system as our run time environment this should yield relatively fast run time processing and provide a more expressive query language in which aggregates and the like can be expressed easily

on relativized polynomial and exponential computations the relationship between polynomial and exponential time bounded relativized computations is investigated it is shown that there exists an oracle x such that relative to x nondeterministic exponential computations yield only the languages in sigma 2 p x from the polynomial hierarchy more informally relative to that x two polynomial quantifiers are as powerful as one exponential quantifier

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

conditional logics of normality a modal approach abstract several conditional theories of default reasoning have recently been proposed for the representation of statements about normal states of affairs or prototypical properties the natural semantics of these systems and their ability to reason about default rules make these approaches quite appealing we present a family of modal logics in which we define a conditional connective for statements of normality and examine its properties we also demonstrate that two of the most important conditional approaches are equivalent to fragments of our conditional logics of normality and to standard modal logics the approach we take is general enough to allow the expression of a number of different forms of defeasible reasoning and can be used to illustrate the relationship between these types of reasoning e g belief revision subjunctive and autoepistemic reasoning and our default logics this relationship is explored in a companion paper

all i know a study in autoepistemic logic abstract current approaches to formalizing nonmonotonic reasoning using logics of belief require the definition of new metalogical properties over sets of sentences this research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic satisfiability validity implication this is done by extending a logic of belief so that it is possible to say that only a certain proposition or finite set of them is believed this research also extends previous approaches to handle quantifiers and equality provides a semantic account of certain types of nonmonotonicity and through a simple proof theory allows formal derivations to be generated

a new technique in the effective field theory of general spin s dilute ising models abstract the effective field equations for diluted spin s ising models are derived using a probability distribution method based on the use of generalized van der waerden identities the approach is employed within the framework of a single site cluster theory based on the use of exact ising spin identities the effective field equations for ising models having all possible single ion and nearest neighbour pair interactions are reported for all spin values from s 1 2 to s 5 2

nonmonotonic logic and temporal projection abstract nonmonotonic formal systems have been proposed as an extension to classical first order logic that will capture the process of human default reasoning or plausible inference through their inference mechanisms just as modus ponens provides a model for deductive reasoning but although the technical properties of these logics have been studied in detail and many examples of human default reasoning have been identified for the most part these logics have not actually been applied to practical problems to see whether they produce the expected results we provide axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning thus presumably amenable to representation in nonmonotonic logic upon examining the resulting nonmonotonic theories however we find that the inferences permitted by the logics are not those we had intended when we wrote the axioms and in fact are much weaker this problem is shown to be independent of the logic used nor does it depend on any particular temporal representation upon analyzing the failure we find that the nonmonotonic logics we considered are inherently incapable of representing this kind of default reasoning the first part of the paper is an expanded version of one that appeared in the 1986 aaai proceedings the second part reports on several responses to our result that have appeared since the original paper was published

mean field renormalization group analysis of the blume capel model the critical properties of the d dimensional blume capel model is studied by using the mean field renormalization group method the phase diagram and tricritical behaviour of the square lattice and various three dimensional lattices have been analysed results are compared with those of high temperature series expansion and variational methods

the expressive power of circumscription abstract circumscription is a form of nonmonotonic reasoning introduced by mccarthy 1997 as a way of characterizing defaults using second order logic the consequences of circumscription are those formulas true in the minimal models under a pre order on models in the case of domain circumscription the pre order was the sub model relation formula circumscription mccarthy 1980 1986 is characterized by minimizing a set of formulas one model is preferred to another model when the extensions of the minimized formulas in the first are subsets of the extensions in the second we show that the propositional version of formula circumscription can capture all pre orders on valuations of finite languages we consider the question of infinite languages and give the corresponding representation theorems we further show that there are natural defaults inertia in temporal projection captured by inductive definitions that cannot be captured by circumscription in the first order case finally contrary to previous claims we show that propositional formula circumscription can capture all preferential consequence relations over finite propositional languages as defined by kraus et al 1990 thus in the finite propositional case there is no restriction on the kinds of preferential defaults that circumscription can describe

on the merging of dung s argumentation systems in this paper the problem of deriving sensible information from a collection of argumentation systems coming from different agents is addressed the underlying argumentation theory is dung s one each argumentation system gives both a set of arguments and the way they interact i e attack or non attack according to the corresponding agent the inadequacy of the simple yet appealing method which consists in voting on the agents selected extensions calls for a new approach to this purpose a general framework for merging argumentation systems from dung s theory of argumentation is presented the objective is achieved through a three step process first each argumentation system is expanded into a partial system over the set of all arguments considered by the group of agents reflecting that some agents may easily ignore arguments pointed out by other agents as well as how such arguments interact with her own ones then merging is used on the expanded systems as a way to solve the possible conflicts between them and a set of argumentation systems which are as close as possible to the whole profile is generated finally voting is used on the selected extensions of the resulting systems so as to characterize the acceptable arguments at the group level

a new semantics for overriding in description logics abstract many modern applications of description logics dls for short such as biomedical ontologies and semantic web policies provide fresh motivations for extending dls with nonmonotonic inferences a topic that has attracted a significant amount of attention along the years despite this nonmonotonic inferences are not yet supported by dl technology due to a number of issues related to expressiveness computational complexity and optimizations this paper contributes to the practical support of nonmonotonic inferences in description logics by introducing a new semantics expressly designed to address knowledge engineering needs this formalism has appealing expressiveness enjoys nice computational properties and constitutes an interesting solution to an ample class of application needs the formalism is validated through extensive comparison with the other nonmonotonic dls and systematic scalability tests the test case generator and its novel validation methodology constitute a further contribution of this paper

any world assumptions in logic programming due to the usual incompleteness of information representation any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information the stable model semantics that has become the dominating approach to give semantics to logic programs relies on the closed world assumption cwa which asserts that by default the truth of an atom is false there is a second well known assumption called open world assumption owa which asserts that the truth of the atoms is supposed to be unknown by default however the cwa the owa and the combination of them are extremal though important assumptions over a large variety of possible assumptions on the truth of the atoms whenever the truth is taken from an arbitrary truth space the topic of this paper is to allow any assignment i e interpretation over a truth space to be a default assumption our main result is that our extension is conservative in the sense that under the everywhere false default assumption cwa the usual stable model semantics is captured due to the generality and the purely algebraic nature of our approach it abstracts from the particular formalism of choice and the results may be applied in other contexts as well

three valued nonmonotonic formalisms and semantics of logic programs abstract we introduce three valued extensions of major nonmonotonic formalisms and we prove that the recently proposed well founded semantics of logic programs is equivalent for arbitrary logic programs to three valued forms of mccarthy s circumscription reiter s closed world assumption moore s autoepistemic logic and reiter s default theory this result not only provides a further justification of the well founded semantics as a natural extension of the perfect model semantics from the class of stratified programs to the class of all logic programs but it also establishes the class of all logic programs as a large class of theories for which natural forms of all four nonmonotonic formalisms coincide it also paves the way for using efficient computation methods developed for logic programming as inference mechanisms for nonmonotonic reasoning

a polynomial jump operator for recursive sets a define a complexity theoretic version of the ordinary recursion theoretic jump by setting a equal to the canonical npa complete set thus a

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

a theorem on the consistency of circumscription abstract this paper gives more general conditions under which mccarthy s circumscription is consistent allowing application of the method outside the domain of universal sentences it is shown that circumscription as presented here continues to correspond to the semantic model of minimization some applications are detailed

blume emery griffiths model on the honeycomb lattice exact results are obtained for a spin 1 system on the honeycomb lattice with the blume emery griffiths hamiltonian kt j i jsisj k i j si2j2 isi2 h si subject to the constraintk ln coshj forj 0 the system behaves like a spin 1 2 ising ferromagnet with the free energy analytic everywhere except at the first order phase boundaryh 0 tanhj 2 e sqrt 3 derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization forj 0 the system can be transcribed into an antiferromagnetic spin 1 2 ising model in a real magnetic field and from this equivalence portions of the exact phase boundary are determined

a theoretical study of the diluted spin 5 2 blume capel model the quenched site diluted spin 52 blume capel model is studied using a new technique in effective field theory that employs a probability distribution within the framework of single site cluster theory based on the use of exact ising spin identities the probability distribution derived with the aid of tucker s generalised van der waerden operators correctly account for the single site kinematic relations and certain configurational averaging identities the concentration dependence of the ferromagnetic phase boundary is studied in particular it is found that a range of single ion field strengths exists over which the critical concentration for ordering varies anomalously results for the honeycomb square and cubic lattices are presented the thermal variation of the magnetization the quadrupolar and higher order magnetization moments are presented for selected values of the concentration

hausdorff dimension and oracle constructions bennett and gill relative to a random oracle a pa npa co npa with probability 1 siam j comput 10 1981 96 113 proved that pa npa relative to a random oracle a or in other words that the set o p np a pa npa has lebesgue measure 0 in contrast we show that o p np has hausdorff dimension 1 this follows from a much more general theorem if there is a relativizable and paddable oracle construction for a complexity theoretic statement then the set of oracles relative to which holds has hausdorff dimension 1 we give several other applications including proofs that the polynomial time hierarchy is infinite relative to a hausdorff dimension 1 set of oracles and that pa npa conpa relative to a hausdorff dimension 1 set of oracles