Explicit belief, Justification terms and Quasi-consistent evidence
Joris A. Galema

Abstract:
Logical omniscience is widely discussed within formal epistemology. An agent is said to be logically omniscient if their knowledge and belief is closed under logical consequence. Such a closure may be an ideal to strive for but, in the interest of modeling realistic agents, is something we may want to avoid. Standard epistemic logics that use possible worlds often have this problem due to inherent properties of such possible worlds semantics. However, such models may also be interpreted differently. As opposed to these beliefs being actual explicit beliefs, one can interpret them as potential implicit beliefs.
When making a distinction between explicit and implicit belief one can take explicit beliefs as fundamental and derive implicit beliefs from these. This can be taken a step further by not merely taking explicit beliefs as fundamental but by considering explicit evidence as fundamental. From these we can then derive explicit belief and in turn implicit belief.
Such explicit evidence can come in the form of formulas, but this can lack expressivity that we may want with the intent of modeling non-omniscient agents. Instead, such explicit evidence may come in the form of justification terms to overcome these limitations.
In this thesis we take inspiration from an existing explicit evidence model and enrich it with justification terms that are able to encode derivations. In this manner we obtain more fine-grained models that are able to provide justifications on how agents’ obtained gained beliefs and update their beliefs on newly acquired evidence.
Furthermore, we provide an axiomatization for the logic of quasi-consistent belief (QCB) and show completeness.