A theoretical grounding is provided for a cooperating knowledge-based systems (CKBS) model which is based upon agents, cooperation blocks, and cooperation block hierarchies. Our model describes the requirements for task decomposition, negotiation, cooperation and coordination, fault tolerance, and recoverability, these requirements in turn defining a holonic system. The behavioral properties of our model are described using state transition diagrams and properties of correctness and termination are proven.

Cyclic covers are shown to characterise disjunctive stable models of unstratified deductive databases, and to facilitate top-down query processing, query compilation and view updating under the disjunctive stable model semantics. Such processing is shown to be more complex than comparable processing of stratified databases.

In this paper, a means of combining several search-space pruning rules, including factorization and circuit, into Bibel's connection method, is considered.

It is a theorem of Prikry [7] that ifκcarries a uniformη-descendingly complete ultrafilter then the stationary reflection property fails. In this paper we will derive similar results, but here from properties of filters (or ideals) rather than ultrafilters. Throughoutκandηwill denote regular cardinals withη<κ(in particularκwill be uncountable), andIwill denote an ideal onκ, by which we mean a setI⊆P(κ) such that (i)Iis closed under taking subsets and finite unions and (ii)αЄIfor eachα<κ, butκ∉I.Iis said to beμ-complete if it is closed under taking unions of size <μ,I* = {X⊆κ∣κ−XЄI} is the filter dual toIand ifAЄI+(=P(κ) −I), thenI∣Ais the ideal onκgiven byI∣A= {X⊆κ∣X∩AЄI}. Ifh: A→κthenhis said to be (i) unbounded modIif for eachα<κ,h−1(α) = {ξЄA∣h(ξ)<α} ЄIand (ii) a least function forIifhis unbounded modIand wheneverg: A→κis a function, unbounded modI, then {ξЄA∣g{ξ)

In this paper we consider the problem of lifting properties of the Fréchet ideal Iκ = {X ⊆ κ: ∣X∣ < κ} on a regular uncountable cardinal κ, to an analogue about Iκλ, the ideal of not unbounded subsets of Pκλ. With this in mind, in §1 we introduce and study the class of seminormal λ-generated ideals on Pκλ. We shall see that ideals belonging to this class display properties which are clearly analogous to those of the Fréchet ideal on κ (for instance, with regard to saturation, normality and weak selectivity) and yet are closely related to Iκλ. Our results here show that if λ<λ = λ, then many restrictions of Iκλ are weakly selective, nowhere precipitous and, quite suprisingly, seminormal (but nowhere normal). These latter two results suggest the question of whether any restriction of Iκλ can ever be normal. In §2 we prove that if κ is strongly inaccessible, λ<κ = 2λ and NSκλ, the ideal of nonstationary subsets of Pκλ, has a mild selective property, then NSκλ∣A = Iκλ∣A for some stationary A ⊆ Pκλ. In [1] Baumgartner showed that if κ is weakly compact and P is the collection of indescribable subsets of κ, then P → (P, κ)2. As a Pκλ analogue of indescribability, Carr (see [3]–[5]) introduced the λ-Shelah property, but was unable to derive the natural Pκλ analogue of Baumgartner's result, (where NShκλ is the normal ideal on Pκλ induced by the λ-Shelah property). In §3 we show that the problem lies in the fact that, as far as we know, NShκλ is not sufficiently distributive, and derive conditions which are sufficient and, in a sense, necessary to yield partitions related to .

It is a theorem of Rowbottom [12] that ifκis measurable andIis a normal prime ideal onκ, then for eachλ<κ, In this paper a natural structural property of ideals, distributivity, is considered and shown to be related to this and other ideal theoretic partition relations. The set theoretical terminology is standard (see [7]) and background results on the theory of ideals may be found in [5] and [8]. Throughoutκwill denote an uncountable regular cardinal, andIa proper, nonprincipal,κ-complete ideal onκ.NSκis the ideal of nonstationary subsets ofκ, andIκ= {X⊆κ∣∣X∣<κ}. IfA∈I+(=P(κ) −I), then anI-partitionofAis a maximal collectionW⊆,P(A) ∩I+so thatX∩ Y ∈IwheneverX, Y∈W, X≠Y. TheI-partitionWis said to be disjoint if distinct members ofWare disjoint, and in this case, for denotes the unique member ofWcontainingξ. A sequence 〈Wα∣α<η} ofI-partitions ofAis said to be decreasing if wheneverα<β<ηandX∈Wβthere is aY∈Wαsuch thatX⊆Y. (i.e.,WβrefinesWα).