We develop a logic for reasoning about semi-public environments , i.e. environments in which a process is executing, and where agents in the environment have partial and potentially different views of the process. Previous work on this problem illustrated that it was problematic to obtain both an adequate semantic model and a language for reasoning about semi-public environments. We here use program models for representing the changes that occur during the execution of a program. These models serve both as syntactic objects and as semantic models, and are a modification of action models in Dynamic Epistemic Logic, in the sense that they allow for ontic change (i.e. change in the world or state). We show how program models can elegantly capture a notion of observation of the environment. The use of these models resolves several difficulties identified in earlier work, and admit a much simpler treatment than was possible in previous work on semi-public environments.

In this paper we attempt to shed light on the concept of an agent's knowledge after a non-deterministic action is executed. We start by making a comparison between notions of non-deterministic choice, and between notions of sequential composition, of settings with dynamic and/or epistemic character; namely Propositional Dynamic Logic (PDL), Dynamic Epistemic Logic (DEL), and the more recent logic of Semi-Public Environments (SPE). These logics represent two different approaches for defining the aforementioned actions, and in order to provide unified frameworks that encompass both, we define the logics DELVO (DEL+Vision+Ontic change) and PDLVE (PDL+Vision+Epistemic operators). DELVO is given a sound and complete axiomatisation.

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Default conditionals are statements that express a condition of normality, in the form 'if ϕ then normally ψ' and are of primary importance in Knowledge Representation. There exist modal approaches to the construction of conditional logics of normality. Most of them are built on notions of preference among possible worlds, corresponding to the semantic intuition that (ϕ ⇒ ψ) is true in a situation if in the most preferred (most 'normal') situations in which ϕ is true, ψ is also true. It has been noticed that there exist natural epistemic readings of a default conditional, but this direction has not been thoroughly explored. A statement of the form 'something known to be a bird, that can be consistently believed to fly, does fly' involves well-known epistemic attitudes and allows the possibility of defining defaults within the rich framework of Epistemic Logic. We pursue this direction here within KBE, a recently introduced S4.2-based modal logic of knowledge, belief and estimation. In this logic, knowledge is a normal S4 operator, belief is a normal KD45 operator and estimation is a non-normal operator interpreted as a 'majority' quantifier over the set of epistemically alternative situations. We define and explore various conditionals using the epistemic operators of KBE, capturing (ϕ ⇒ ψ) in various ways, including 'it is known that assuming ϕ allows us to assume ϕ ∧ ψ' or 'if ϕ is known and there is no reason to believe ¬ψ then ψ can be plausibly inferred'. Overall, we define here two weak nonmonotonic default conditionals, one monotonic conditional and two stronger nonmonotonic conditionals without axiom ID. Our results provide concrete evidence that the machinery of epistemic logic can be exploited for the study of default conditionals.