Catálogo de publicaciones - libros

The following remarks are going to suggest that there is more at stake in the current controversy over conditionals than merely the logic of conditionals. Among the more general issues involved are the limits of truth-conditionality, the implications of this for certain programs in the philosophy of language, the values of truth and probability, and the rationale of logic [and, incidentally, the foundations of probability and decision theory as well, but I won’t get into that].

Various controversies surrounding the meaning of conditionals like “A given B” or “if B then A” are discussed including that they can non-trivially carry the standard conditional probability, are truth functional but have three rather than two truth values, are logically and probabilistically non-monotonic, and can be combined with operations that extend the standard Boolean operations. A new theory of deduction with uncertain conditionals extends the familiar equations that define deduction between Boolean propositions. Several different deductive relations arise leading to different sets of implications. New methods to determine these implications for one or more conditionals are described. An absent-minded coffee drinker example containing two subjunctive (counter-factual) conditionals is solved. The use of information entropy to cut through complexity, and the question of the confidence to be attached to a maximum entropy probability distribution, are discussed including the results of E. Jaynes concerning the concentration of distributions at maximum entropy.

This paper bridges the gap between comparative belief structures, such as those induced by probability measures, and logical representations of accepted beliefs. We add, to natural properties of comparative belief relations, some conditions that ensure that accepted beliefs form a deductively closed set. It is shown that the beliefs accepted by an agent in all contexts can always be described by a family of conditionals. These results are closely connected to the nonmonotonic ’preferential’ inference system of Kraus, Lehmann and Magidor and the works of Friedman and Halpern on their so-called plausibility functions. Acceptance relations are also another way of approaching the theory of belief change after the works of Gärdenfors and colleagues.

Processes that govern the interpretation of conditional statements by lay reasoners are considered a key-issue by nearly all reasoning psychologists. An argumentative approach to interpretation is outlined, based on the idea that one has to retrieve the intention of the speaker to interpret a statement, and an argumentative based typology of conditionals is offered. Some empirical support to the approach is provided, as well as some theoretical support from an evolutionary perspective.

We show how to extract iterated revision strategies for complex evidence, e.g. epistemic conditionals, from reasonable default inference notions. This approach allows a more extensive cross-fertilization between default reasoning and belief revision. To illustrate it, we use powerful default formalisms exploiting canonical ranking constructions, like system JZ, for specifying new ranking-based revision mechanisms. They extend Spohn’s ranking revision to sets of conditionals and satisfy basic rationality principles.

We look at iterated non-prioritised belief revision, using as a starting point a model of non-prioritised revision, similar to Makinson’s , which assumes an agent keeps a set of beliefs whose function is to block certain revision inputs. We study postulates for the iteration of this operation. These postulates generalise some of those which have previously been proposed for iterated AGM (“prioritised”) revision, including those of Darwiche and Pearl. We then add a second type of revision operation which allows the core itself to be revised. Postulates for the iteration of this operator are also provided, as are rules governing mixed sequences of revisions consisting of both regular and core inputs. Finally we give a construction of both a regular and core revision operator based on an agent’s . This construction is shown to satisfy most of the postulates.

A logical framework that emphasizes the impact of assertions is investigated with respect to providing an interpretation for conditionals and defaults. We consider theories consisting essentially of monadic subsumption statements.For every such theory there is an associated ordered by a . We show how to naturally interpret in this information domain. Moreover, we study several ways to cope with . In particular, we adapt the approaches of Poole and Reiter to our framework.

We present a Maple package for experimenting with conditional event algebras of Schay, Adams-Calabrese, Goodman-Nguyen-Walker and Product Space of Goodman and Nguyen.

It includes the implementation of the first polynomial time algorithm for calculating probabilities in the product space conditional event algebra.

Inference among the conditional independences in nondegenerate Gaussian vectors is studied by algebraic techniques. A general method to prove implications involving the conditional independences is presented. The method relies on computations of a Groebner basis. Examples of the implications are discussed.

We show how probabilistic logic and probabilistic conditional logic can be formalized in the framework of institutions, thereby supporting the study of structural properties of both syntax and semantics of these logics. By using the notions of institution morphism and institution embedding, the relationships between probabilistic propositional logic, probabilistic conditional logic, and the underlying two-valued propositional logic are investigated in detail, telling us, for instance, precisely how to interpret probabilistic conditionals as probabilistic facts or in a propositional setting and vice versa.