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Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct ...φ intuitively expressing that \after every public announcement of a formula, formula φ is true". The logic APAL is undecidable and it has an infinitary axiomatization. Now consider restricting the APAL quantification to public announcements of Boolean formulas only, such that ...φ intuitively expresses that \after every public announcement of a Boolean formula, formula φ is true". This logic can therefore be called Boolean arbitrary public announcement logic, BAPAL. The logic BAPAL is the subject of this work. Unlike APAL it has a infinitary axiomatization. Also, BAPAL is not at least as expressive as APAL. A further claim that BAPAL is decidable is deferred to a companion paper. [ABSTRACT FROM AUTHOR]

RoCTL* was proposed to model and specify the robustness of reactive systems. RoCTL* extended CTL* with the addition of Obligatory and Robustly operators, which quantify over failure-free paths and paths with one more failure, respectively. This article gives an axiomatization for all the operators of RoCTL* with the exception of the Until operator; this fragment is able to express similar contrary-to-duty obligations to the full RoCTL* logic. We call this formal system NORA, and give a completeness proof. We also consider the fragments of the language containing only path quantifiers but where atoms are dependent on histories. We examine semantic properties and potential axiomatizations for these fragments. [ABSTRACT FROM AUTHOR]

We examine various logics that combine knowledge, awareness, and change of awareness. An agent can become aware of propositional propositions but also of other agents or of herself. The dual operation to becoming aware, forgetting, can also be modelled. Our proposals are based on a novel notion of structural similarity that we call awareness bisimulation, the obvious notion of modal similarity for structures encoding knowledge and awareness. [ABSTRACT FROM AUTHOR]

In this paper we study sublogics of RoCTL*, a recently proposed logic for specifying robustness. RoCTL* allows specifying robustness in terms of properties that are robust to a certain number of failures. RoCTL* is an extension of the branching time logic CTL* which in turn extends CTL by removing the requirement that temporal operators be paired with path quantifiers. In this paper we consider three sublogics of RoCTL*. We present a tableau for RoBCTL*, a bundled variant of RoCTL* that allows fairness constraints to be placed on allowable paths. We then examine two CTL-like restrictions of CTL*. Pair-RoCTL* requires a temporal operator to be paired with a path quantifier; we show that Pair-RoCTL* is as hard to reason about as the full CTL*. State-RoCTL* is restricted to State formulas, and we show that there is a linear truth preserving translation of State-RoCTL into CTL, allowing State-RoCTL to be reasoned about as efficiently as CTL. [ABSTRACT FROM AUTHOR]