We give a probabilistic interpretation of first-order formulas based on Valiants model of pac-learning. We study the resulting notion of probabilistic or approximate truth and take some first steps in developing its model theory. In particular we show that every fixed error parameter determining the precision of universal quantification gives rise to a different class of tautologies. Finally we...

There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, xpoint theory, and proof theory for TPLPs, and show that the xpoint theory may be used to enumerate consequences of a TPLP in a sound and ...

1 CHARLES RIVER ANALYTICS, Cambridge, MA 02138, USA Abstract We present a logic for reasoning with probabilistic arguments to help decision making under uncertainty. The syntax of the logic is essentially modal propositional, and arguments of decision makers are expressed as sentences of the logic, with associated supports drawn from a probability dictionary. To aggregate a set of arguments for...

In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to spec­ ify the probability structure. We consider the case in which probabilistic information is not available. Instead of using probability intervals, we allow for the specification of the probabilities of disjunctions. Because mini­ mal ...

Recent research has shown there are two types of uncertainty that can be expressed in first-order logic— propositional and statistical uncertainty—and that both types can be represented in terms of probability spaces. However, these efforts have fallen short of providing a general account of how to design probability measures for these spaces; as a result, we lack a crucial component of any sys...

This paper presents a probabilistic extension of Neighbourhood Logic (NL,[14, 1]). The study of such an extension is motivated by the need to supply the Probabilistic Duration Calculus (PDC, [10, 4]) with a proof system. The relation between the new logic and PDC is similar to that between DC [15] and ITL [12, 3]. We present a complete proof system for the new logic.

The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC ) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem for the system of probabilistic ITL with respect to an abstract semantics and a relative completeness theorem for the system of probabilistic DC with respect ...