The temporal calculus of conditional objects and conditional events (original) (raw)
Related papers
A history and introduction to the algebra of conditional events and probability logic
IEEE Transactions on Systems, Man, and Cybernetics, 1994
This article is meant to serve as an introduction to the following series of papers on various aspects of conditional event algebra and probability logic. It addresses the history of the problem and gives an overview of the development of the subject and its impact on the investigation of problems within AI.
On the logic of nonmonotonic conditionals and conditional probabilities
Journal of Philosophical Logic, 1996
In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.
A logic for reasoning about probabilities
Information and Computation, 1990
ABOUT PROBABILITIES 81 pendently of ous) can be extended in a straightforward way to the language of our first logic. The measurable case of our richer logic bears some similarities to the first-order logic of probabilities considered by Bacchus [Bac88]. There are also some significant technical differences; we compare our work with that of Bacchus and the more recent results on first-order logics of probability in [AH89, Ha1891 in more detail in Section 6.
A logic for probabilities in semantics
2002
Probabilistic computation has proven to be a challenging and interesting area of research, both from the theoretical perspective of denotational semantics and the practical perspective of reasoning about probabilistic algorithms. On the theoretical side, the probabilistic powerdomain of Jones and Plotkin represents a significant advance. Further work, especially by Alvarez-Manilla, has greatly improved our understanding of the probabilistic powerdomain, and has helped clarify its relation to classical measure and integration theory. On the practical side, many researchers such as Kozen, Segala, Desharnais, and Kwiatkowska, among others, study problems of verification for probabilistic computation by defining various suitable logics for the classes of processes under study. The work reported here begins to bridge the gap between the domain theoretic and verification (model checking) perspectives on probabilistic computation by exhibiting sound and complete logics for probabilistic powerdomains that arise directly from given logics for the underlying domains. The category in which the construction is carried out generalizes Scott's Information Systems by taking account of full classical sequents. Via Stone duality, following Abramsky's Domain Theory in Logical Form, all known interesting categories of domains are embedded as subcategories. So the results reported here properly generalize similar constructions on specific categories of domains. The category offers a promising universe of semantic domains characterized by a very rich structure and good preservation properties of standard constructions. Furthermore, because the logical constructions make use of full classical sequents, the morphisms have a natural non-deterministic interpretation. Thus the category is a natural one in which to investigate the relationship between probabilistic and non-deterministic computation. We discuss the problem of integrating probabilistic and non-deterministic computation after presenting the construction of logics for probabilistic powerdomains.
On the Algebraic Structure of Conditional Events
Lecture Notes in Computer Science, 2015
This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts.
A logic for reasoning about probabilities* 1
Information and computation, 1990
ABOUT PROBABILITIES 81 pendently of ous) can be extended in a straightforward way to the language of our first logic. The measurable case of our richer logic bears some similarities to the first-order logic of probabilities considered by Bacchus [Bac88]. There are also some significant technical differences; we compare our work with that of Bacchus and the more recent results on first-order logics of probability in [AH89, Ha1891 in more detail in Section 6.
On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic
Journal of Philosophical Logic, 1998
In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.
CP-logic: A Language of Causal Probabilistic Events and Its Relation to Logic Programming
Theory and Practice of Logic Programming, 2009
We examine the relation between constructive processes and the concept of causality. We observe that causality has an inherent dynamic aspect, i.e., that, in essence, causal information concerns the evolution of a domain over time. Motivated by this observation, we construct a new representation language for causal knowledge, whose semantics is defined explicitly in terms of constructive processes. This is done in a probabilistic context, where the basic steps that make up the process are allowed to have non-deterministic effects. We then show that a theory in this language defines a unique probability distribution over the possible outcomes of such a process. This result offers an appealing explanation for the usefulness of causal information and links our explicitly dynamic approach to more static causal probabilistic modeling languages, such as Bayesian networks. We also show that this language, which we have constructed to be a natural formalization of a certain kind of causal statements, is closely related to logic programming. This result demonstrates that, under an appropriate formal semantics, a rule of a normal, a disjunctive or a certain kind of probabilistic logic program can be interpreted as a description of a causal event. * Research supported by GOA 2003/8 Inductive Knowledge Bases and by FWO Vlaanderen. † Joost Vennekens is a postdoctoral researcher of the FWO.
Journal of Computer and System Sciences, 1984
A logic, PrDL, is presented, which enables formal reasoning about probabilistic programs or, alternatively, reasoning probabilistically about conventional programs. The syntax of PrDL derives from Pratt's first-order dynamic logic and the semantics extends Kozen's semantics of probabilistic programs. An axiom system for PrDL is presented and shown to be complete relative to an extension of first-order analysis. For discrete probabilities it is shown that first-order analysis actually suffkes. Examples are presented, both of the expressive power of PrDL, and of a proof in the axiom system.