Belief Revision in Science: Informational Economy and Paraconsistency

In the present paper, our objective is to examine the application of belief revision models to scientific rationality. We begin by considering the standard model AGM, and along the way a number of problems surface that make it seem inadequate for this specific application. After considering three different heuristics of informational economy that seem fit for science, we consider some possible adaptations for it and argue informally that, overall, some paraconsistent models seem to better satisfy these principles, following Testa (2015). These models have been worked out in formal detail by Testa, Cogniglio, & Ribeiro (2015, 2017)

A Dynamic Solution to the Problem of Logical Omniscience

The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the laws of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent

Logic, self-awareness and self-improvement: The metacognitive loop and the problem of brittleness

This essay describes a general approach to building perturbation-tolerant autonomous systems, based on the conviction that artificial agents should be able notice when something is amiss, assess the anomaly, and guide a solution into place. We call this basic strategy of self-guided learning the metacognitive loop; it involves the system monitoring, reasoning about, and, when necessary, altering its own decision-making components. In this essay, we (a) argue that equipping agents with a metacognitive loop can help to overcome the brittleness problem, (b) detail the metacognitive loop and its relation to our ongoing work on time-sensitive commonsense reasoning, (c) describe specific, implemented systems whose perturbation tolerance was improved by adding a metacognitive loop, and (d) outline both short-term and long-term research agendas

Cognitive context and arguments from ontologies for learning

The deployment of learning resources on the web by different experts has resulted in the accessibility of multiple viewpoints about the same topics. In this work we assume that learning resources are underpinned by ontologies. Different formalizations of domains may result from different contexts, different use of terminology, incomplete knowledge or conflicting knowledge. We define the notion of cognitive learning context which describes the cognitive context of an agent who refers to multiple and possibly inconsistent ontologies to determine the truth of a proposition. In particular we describe the cognitive states of ambiguity and inconsistency resulting from incomplete and conflicting ontologies respectively. Conflicts between ontologies can be identified through the derivation of conflicting arguments about a particular point of view. Arguments can be used to detect inconsistencies between ontologies. They can also be used in a dialogue between a human learner and a software tutor in order to enable the learner to justify her views and detect inconsistencies between her beliefs and the tutor’s own. Two types of arguments are discussed, namely: arguments inferred directly from taxonomic relations between concepts, and arguments about the necessary an

AGM-Like Paraconsistent Belief Change

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations

On Conceiving the Inconsistent

This work has been developed within the 2013–15 ahrc project The Metaphysical Basis of Logic: The Law of Non-Contradiction as Basic Knowledge (grant ref. ah/k001698/1). A version of the paper was presented in September 2013 at the Modal Metaphysics Workshop in Bratislava. I am grateful to the audiences there and at the Aristotelian Society meeting for many helpful comments and remarks.Peer reviewedPostprin

A Parameterised Hierarchy of Argumentation Semantics for Extended Logic Programming and its Application to the Well-founded Semantics

Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships between the semantics and examine some essential properties concerning consistency and the coherence principle, which relates default negation and explicit negation. Most significantly, we place existing semantics put forward in the literature in our hierarchy and identify a particular argumentation semantics for which we prove equivalence to the paraconsistent well-founded semantics with explicit negation, WFSX$_p$. Finally, we present a general proof theory, based on dialogue trees, and show that it is sound and complete with respect to the argumentation semantics.Comment: To appear in Theory and Practice of Logic Programmin