ABSTRACT. Rational agents must have some internal representation of their knowledge or belief system. Belief Revision is a research area that aims at understanding how they should change their representations when they are faced with new information. In a contraction operation, a sentence is removed from a knowledge base and must not be logically entailed by the resulting set. Pseudo-contraction was proposed by Hansson as an alternative to base contraction where some degree of syntax independence is allowed. In this work, we analyse kernel constructions for pseudo-contraction operations and their formal properties. Also, we show the close relationship between concepts and definitions of Belief Revision and Ontology Repair (such as pseudo-contractions and gentle repairs, respectively).

ABSTRACT. Trust plays a role in the process of belief revision. When information is reported by another agent, it should only be believed if the reporting agent is trusted as an authority over some relevant domain. In practice, an agent will be trusted on a particular topic if they have provided accurate information on that topic in the past. In this paper, we demonstrate how an agent can construct a model of knowledge-based trust based on the accuracy of past reports. We then show how this model of trust can be used in conjunction with Ordinal Conditional Functions to define two approaches to trust-influenced belief revision. In the first approach, strength of trust and strength of belief are assumed to be incomparable as they are on different scales. In the second approach, they are aggregated in a natural manner. We then describe a software tool for modelling and reasoning about trust and belief change. Our software allows a trust graph to be updated incrementally by looking at the accuracy of past reports. After constructing a trust graph, the software can then compute the result of AGM-style belief revision using two different approaches to incorporating trust.

ABSTRACT. We study what can be learned when receiving reports from multiple non-expert information sources. We suppose that sources report all that they consider possible, given their expertise. This may result in false and inconsistent reports when sources lack expertise on a topic. A learning method is truth-tracking, roughly speaking, if it eventually converges to correct beliefs about the ``actual" world. This involves finding both the actual state of affairs in the domain described by the sources, and finding the extent of the expertise of the sources themselves. We investigate the extent to which truth-tracking is possible, and describe what information can be learned even if the actual world cannot be pinned down uniquely. We find that a broad spread of expertise among the sources allows the actual state of affairs to be found, even if no individual source is an expert on all topics. On the other hand, narrower expertise at the individual level allows the actual expertise to be found more easily. Finally, we turn to concrete families of learning methods adapted from the belief change literature, and characterise the conditions under which they are truth-tracking.

ABSTRACT. Empirical methods have been used to test whether human reasoning conforms to models of reasoning in logic-based artificial intelligence. This work investigates through surveys whether postulates of belief revision and update are plausible with human reasoners. The results show that participants' reasoning tend to be consistent with the postulates of belief revision and belief update when judging the premises and conclusion of the postulate separately.

ABSTRACT. Lexicographic inference is a well-behaved and popular approach to reasoning with non-monotonic conditionals. In recent work we have shown that lexicographic inference satisfies syntax splitting, which means we can restrict our attention to parts of the belief base that share atoms with a given query. In this paper, we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference satisfies conditional syntax splitting, and connect conditional independence to several known properties from the literature on non-monotonic reasoning, including the drowning effect.

ABSTRACT. Conditionals are useful for modelling many forms of everyday human reasoning, but are not always sufficiently expressive for representing the information we want to reason about. Here we make the case for a form of situated conditional. By ‘situated’ we mean that there is a context, based on an agent’s beliefs and expectations, that works as background information in evaluating a conditional. These conditionals are able to distinguish, for example, between expectations and counterfactuals. We show that situated conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals, and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates. With the semantics in place, we proceed to define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure and is inspired by the well-known notion of rational closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks.

ABSTRACT. The paper (under review) investigates the impact of weakened forms of transitivity of the betterness relation on the logic of conditional obligation, originating from the work of Hansson, Lewis, and others. These weakened forms of transitivity are well-known from the rational choice theory literature, and include: quasi-transitivity, Suzumura consistency, a-cyclicity, and interval order.