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Title: Modal logics of partial observability
Author: Moyzes, C.
ISNI:       0000 0004 7970 4659
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2019
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This thesis examines the notion of "vision" and how it can be integrated into the established formalism of dynamic and/or epistemic propositional logics. First a logic is developed 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. Here, the use of Program Models is introduced 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 of 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 what was possible in previous work on semi-public environments. It soon becomes apparent that while non-deterministic choice is handled intuitively in program models, it is nonetheless treated differently than in traditional formalisms. To shed light on these concepts 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 aforementioned logic of Semi-Public Environments (SPE). These logics indeed 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 then given a sound and complete axiomatisation. Furthermore, we fill an important gap in the literature by providing complexity results for the satisfiability and model checking problems of DEL, especially for the case of single-agent DEL. Considering DELVO to be a more contemporary version of DEL, we move on to expand these results for DELVO as well. For both logics and for any number of agents, the satisfiability is proven to be in NEXPTIME, while model checking is proven to be in PSPACE.
Supervisor: Van Der Hoek, Wiebe ; Grossi, Davide Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral