Willem Labuschagne

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.

Semantics for Dual Preferential Entailment

We introduce and explore the notion of duality for entailment relations induced by preference orderings on states. We discuss the relationship between these preferential entailment relations from the perspectives of Boolean algebra, inference rules, and modal axiomatisation. Interpreting the preference relations as accessibility relations establishes modular Gödel-Löb logic as a suitable modal framework for rational preferential reasoning.

Natural and artificial cognition: On the proper place of reason

Abstract We explore the psychological foundations of Logic and Artificial Intelligence, touching on representation, categorisation, heuristics, consciousness, and emotion. Specifically, we challenge Deimett’s view of the brain as a syntactic engine that is limited to processing symbols according to their structural properties. We show that cognitive psychology and neurobiology support a dual-process model in which one form of cognition is essentially semantical and differs in important ways from the operation of a syntactic engine. The dual-process model illuminates two important events in Logic and Artificial Intelligence, namely the emergence of non-monotonicity and of embodiment, events that changed the traditional paradigms of ‘Logic = the study of deductive inference’ and ‘Symbolic AI’.

Templated revision

In this paper we study the epistemic change operation of revision when the epistemic state of an agent is extended to include not only beliefs but knowledge too. An information-theoretic model of epistemic states is defined based on the notion of a templated ordering. A set of rationality postulates is defined for templated revision, which extends the AGM postulates, and a model-based representation result is provided characterising the proposed postulates. These postulates capture the intuition that during a revision, the agents knowledge should grow monotonically while the agents belief may grow nonmonotonically. It is shown that templated revision satisfies all the Darwiche-Pearl postulates for iterated revision, except for the controversial postulate (C2).

Supraclassical Consequence Relations

We explore a family of supraclassical consequence relations obtained by varying the criteria according to which counterexamples to classical entailment may be deemed tolerable. This provides a different perspective on the rational consequence relations of nonmonotonic logic, as well as introducing new kinds of entailment with a diversity of poten- tial contextual applications.

Boolean Prediction Analysis under Scrutiny

Boolean Prediction Analysis is a method, based on Boolean algebra, for deriving prediction equations. This study examines some limitations of the method and adapts the method accordingly. The modification is achieved with the aid of a probabilistic measure of relevance, which also constitutes a simple tool for determining whether, and how, continuous variables can be dichotomized so as to render Boolean Prediction Analysis applicable. An illustrative application of the new technique is presented for purposes of comparison with the original approach.