In Artificial Intelligence, abduction is often formalized in first-order logic. In this article, we focus on the problem of identifying equivalence of two abductive theories represented in first-order logic. To this end, two definitions of equivalence are given for abduction. Explainable equivalence requires that two abductive theories have the same explainability for any observation. On the other hand, explanatory equivalence guarantees that any observation has exactly the same explanations in each abductive theory. Explanatory equivalence is a stronger notion than explainable (...) equivalence. In first-order logic, explainable equivalence can be veri.ed by the notion of extensional equivalence in default theories, while explanatory equivalence reduces to logical equivalence between background theories. We also show the complexity results for abductive equivalence. (shrink)

Information is a notion of wide use and great intuitive appeal, and hence, not surprisingly, different formal paradigms claim part of it, from Shannon channel theory to Kolmogorov complexity. Information is also a widely used term in logic, but a similar diversity repeats itself: there are several competing logical accounts of this notion, ranging from semantic to syntactic. In this chapter, we will discuss three major logical accounts of information.

I will analyse three fundamental ways of governing ignorance though abduction, which are essential from an eco-cognitive and eco-logical point of view, in which the central role in human cognition of natural and artefactual environment is taken into account. First of all, according to the so-called GW-schema, proposed by Gabbay and Woods, abduction presents an ignorance-preserving or (ignorance-mitigating) character: given the fact that the abduced hypotheses aim at becoming truths, the basic ignorance is neither solved nor left untouched. Second, I (...) will contend that abduction is not always ignorance preserving but also knowledge enhancing. Indeed, according to the eco-cognitive model of abduction, I myself have recently proposed, we can easily see that, occasionally, knowledge can be immediately increased (and ignorance ‘killed’) through abduction: in this perspective, abduction does not have to be rigidly conceptualized as an inference to the best explanation in the received sense, which is as an inference that, to grant truth, also takes advantage of an empirical evaluation phase or an inductive phase, as Peirce classified it. Finally, it is important to stress that abductive cognition is at the roots of two fundamental cognitive processes. On one side, abductive cognition constructs (and/or takes advantage of the exploitation of) embodiments, external representations, enactions, artefacts and props, which involve ignorant entities suitably transformed in cognitive representations and/or devices. On the other side, abductive cognition dominates those ‘special’ cognitive creative processes that lead to what I call the disseminated ‘computational domestication of ignorant entities’: I will illustrate the example of the recent unconventional computational domestication of ignorant entities, which creates novel cognitive embodiments (morphological computation). (shrink)

Constructing an intuitive theory from data confronts learners with a “chicken‐and‐egg” problem: The laws can only be expressed in terms of the theory's core concepts, but these concepts are only meaningful in terms of the role they play in the theory's laws; how can a learner discover appropriate concepts and laws simultaneously, knowing neither to begin with? We explore how children can solve this chicken‐and‐egg problem in the domain of magnetism, drawing on perspectives from computational modeling and behavioral experiments. We (...) present 4‐ and 5‐year‐olds with two different simplified magnet‐learning tasks. Children appropriately constrain their beliefs to two hypotheses following ambiguous but informative evidence. Following a critical intervention, they learn the correct theory. In the second study, children infer the correct number of categories given no information about the possible causal laws. Children's hypotheses in these tasks are explained as rational inferences within a Bayesian computational framework. (shrink)

An agent-centered, goal-directed, resource-bound logic of human reasoning would do well to note that individual cognitive agency is typified by the comparative scantness of available cognitive resources—information, time, and computational capacity, to name just three. This motivates individual agents to set their cognitive agendas proportionately, that is, in ways that carry some prospect of success with the resources on which they are able to draw. It also puts a premium on cognitive strategies which make economical use of those resources. These (...) latter I callscant-resource adjustment strategies,and they supply the context for an analysis of abduction. The analysis is Peircian in tone, especially in the emphasis it places on abduction’signorance-preservingcharacter. My principal purpose here is to tie abduction’s scarce-resource adjustment capacity to its ignorance preservation. (shrink)

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision (...) for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation. (shrink)

In this paper I argue for a place for logic inscientific methodology, at the same level asthat of computational and historicalapproaches. While it is well known that a awhole generation of philosophers dismissedLogical Positivism (not just for the logicthough), there are at least two reasons toreconsider logical approaches in the philosophyof science. On the one hand, the presentsituation in logical research has gone farbeyond the formal developments that deductivelogic reached last century, and new researchincludes the formalization of several othertypes of (...) reasoning, like induction andabduction. On the other hand, we call for abalanced Philosophy of Science, one inwhich both methods, the formal and thehistorical may be complementary, togetherproviding a pluralistic view of science, inwhich no method is the predominant one. (shrink)

So-called ‘reified temporal logics’ were introduced by researchers in Artificial Intelligence (AI) in the early 1980s, and gave rise to a long-running series of debates concerning the proper way to represent states, events, causation, action, and other notions identified as crucial to the knowledge representation needs of AI. These debates never resulted in a definitive resolution of the issues under discussion, and indeed continue to produce aftershocks to the present day; none the less, we are now sufficiently far removed in (...) time from their heyday for it to be a worthwhile exercise to stand back and review them as a connected piece of history. (shrink)

During the second half of the last century, the importance of serendipitous events in scientific frameworks has been progressively recognized, fueling hard debates about their role, nature, and structure in philosophy and sociology of science. Alas, while discussing the relevance of the topic for the comprehension of the nature of scientific discovery, the philosophical literature has hardly paid attention to the cognitive significance of serendipity, accepting rather than examining some of its most specific features, such as its game-changing effect, the (...) unexpectedness of its occurrence, and its affinity with the concept of “luck”. Thus, in this paper we aim at analyzing these characteristics in the light of their cognitive implications in the recognition, performance, and possible stimulation of serendipitous events in relation to scientific discoveries. (shrink)