The article studies common knowledge in communication networks with a fixed topological structure. It introduces a non-trivial principle, called the Ryōan-ji axiom, which captures logical properties of common knowledge of all protocols with a given network topology. A logical system, consisting of the Ryōan-ji axiom and two additional axioms, is proven to be sound and complete.

Possible-world semantics are provided for Parikh’s relevance-sensitive model for belief revision. Having Grove’s system-of-spheres construction as a base, we consider additional constraints on measuring distance between possible worlds, and we prove that, in the presence of the AGM postulates, these constraints characterize precisely Parikh’s axiom (P). These additional constraints essentially ...

In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X , ω1,...

We show how to automatically generate analytic hypersequent calculi for a large class of logics containing the linearity axiom (lin) (A ⊃ B) ∨ (B ⊃ A) starting from existing (single-conclusion) cut-free sequent calculi for the corresponding logics without (lin). As a corollary, we define an analytic calculus for Strict Monoidal T-norm based Logic SMTL.

We study type spaces where a player’s type at a state is a conditional probability on the space. We axiomatize these type spaces using conditional belief operators, and examine three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certain of her beliefs. Second, echo, according to which the unconditional beliefs implied by the condi...

In general, Policy-based approaches play an important role in the management of web services, for instance, in the choice of semantic web service and quality of services (QoS) in particular. The present research work illustrates a procedure for the web service selection among functionality similar web services based on WS-Policy semantic matching. In this study, the procedure of WS-Policy publi...

This paper considers Kripke completeness of Nelson’s constructive predicate logic N3 and its several variants. N3 is an extension of intuitionistic predicate logic Int by an contructive negation operator ∼ called strong negation. The variants of N3 in consideration are by omitting the axiom A → (∼A → B), by adding the axiom of constant domain ∀x(A(x) ∨ B) → ∀xA(x) ∨ B, by adding (A → B) ∨ (B → ...

PHYSICAL TRACES SAMSON ABRAMSKY AND BOB COECKE Abstract. We revise our ‘Physical Traces’ paper [Abramsky and Coecke CTCS‘02] in the light of the results in [Abramsky and Coecke LiCS‘04]. The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite projector and inner product to be defined, and their key properties to be proved. In this pape...

This paper investigates the univalence axiom in intensional Martin-Löf type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various published and unpublished sources; we then we present a new decomposition of the univalence axiom into simpler axioms. We argue that these axioms are easier to verify...

We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.