0. Introduction 1 1. Background on infinitary logic 2 1.1. Expressive power of Lω1ω 2 1.2. The back-and-forth construction 3 1.3. The Scott isomorphism theorem 4 1.4. ω-logic 7 1.5. Familiar theorems 8 1.6. Failure of compactness 9 2. Background on admissible sets 10 2.1. ∆0 formulas and Σ-formulas in set theory 10 2.2. Axioms of KP 11 2.3. Examples of admissible sets 12 2.4. The admissible set...

Most theorems have more than one proof and most theories have more than one axiomatization. Certain proofs or axiomatizations are preferable to others because they are shorter or more transparent or for some other reason. Our aim is to describe or study the possible proofs of a theorem or the possible axiomatizations of a theory. As the former is a special instance of the latter, by considering...

Visser’s rules form a basis for the admissible rules of IPC. Here we show that this result can be generalized to arbitrary intermediate logics: Visser’s rules form a basis for the admissible rules of any intermediate logic L for which they are admissible. This implies that if Visser’s rules are derivable for L then L has no non-derivable admissible rules. We also provide a necessary and suffici...

Best-response sets (Pearce [29, 1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger-Friedenberg-Keisler [18, 2008]) characterizes “rationality and common assumption of rationality.” We analyze the behavior of SAS’s in some ga...

In this article we address the issue of con dentiality of information in the context of downgrading systems i.e. systems admitting information ow between secrecy levels only through a downgrader. Inspired by the intuition underlying the usual de nition of admissible information ow, we propose an analogue based on trace equivalence as developed in the context of concurrency theory and on a modi ...

As partial justification of their framework for iterated belief revision Darwiche and Pearl convincingly argued against Boutilier’s natural revision and provided a prototypical revision operator that fits into their scheme. We show that the Darwiche-Pearl arguments lead naturally to the acceptance of a smaller class of operators which we refer to as admissible. Admissible revision ensures that ...

We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP -hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC ) is in coNE , thus obtaining a sharp complexity estimate for admissibility in...

We develop a criterion for coalition formation among goal-directed agents, the indecomposable do-ut-des property. The indecomposable do-ut-des property refines the do-ut-des property (literally give to get) by considering the fact that agents prefer to form coalitions whose components cannot be formed independently. A formal description of this property is provided as well as an analysis of alg...

We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a finite number of Möbius transformations. We regard certain sets of Möbius transformations as a generalized notion of digits and introduce sufficient conditions that such a “digit set” yields an admissible representation of [0,+∞]. Furthermore we establish the productivity ...

1.Introduction. Let M be a C∞ -manifold and TM the total space of the tangent bundle. A control system is a subset V ⊂ TM. Fix an initial point q0 ∈ M and a segment [0, t] ⊂ R. Admissible trajectories are Lipschitzian curves q(τ), 0 ≤ τ ≤ t, q(0) = q0, satisfying a differential equation of the form (1) q̇ = vτ (q), where vτ (q) ∈ V ∩ TqM, ∀q ∈ M, vτ (q) is smooth in q, bounded and measurable in ...