An Analysis of First-Order Logics of Probability

By Joseph Y. Halpern. 1989

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Citations in the corpus

Towards Deep Symbolic Reinforcement Learning (2016, methodology): “To handle uncertainty, we propose probabilistic ﬁrst-order logic for the semantic under-pinnings of the low-dimensional conceptual state space representation into which the neural front end must map the system’s high-dimensional raw input [26].”
First-order probabilistic inference (2003, background): “In terms of the first-order probability of Halpern [1990] , the probabilities are all degrees of belief, not statistical assertions about proportions of a population.”
Recognizing textual entailment: Rational, evaluation and approaches – Erratum (2010, background): “There is also a considerable amount of classical work on fuzzy or uncertain inference (e.g. Bacchus 1990; Halpern 1990; Keefe and Smith 1997).”
Quantum Computation and Information (2006, background): “For example, the domains of first-order structures are endowed with probability measures in [44].”
Towards a theory of semantic communication (2011, background): “When we talk about probability of a logical sentence, it should be noted there are two types of probabilities [26].”
Identifiability of Path-Specific Effects (2005, unknown): “If we consider each value assignment u as apossible world, then we can view P (u) as describing our degree of belief that a particular world is true, andP (α) as our belief that a particular statement is true in our causal m odel if viewed as atype 2 probability structure [5].”
Reasoning about Probabilities in Dynamic Systems using Goal Regression (2013, methodology): “15Moreover, the BHL model is compatible with a wide variety of formalisms such as (Fagin and Halpern, 1994; Halpern and Tuttle, 1993; Halpern, 1990).”
A Logical Theory of Localization (2015, background): “Logical formalisms for probabilistic reasoning, such as [1,27], are equipped to handle features such as disjunctions and quantiﬁers, but they do not explicitly address actions.”
Defining Explanation in Probabilistic Systems (1997, background): “(This type of model is also considered in (Halpern 1990), wbere a structure con sists of possible worlds, with a distribution over the worlds, and, in each world there is a distribution on the individuals in that world; a formal language is provided for reasoning about such models.”
The Third PASCAL Recognizing Textual Entailment Challenge (2007, background): “[1], [8], [9]), yet, making significant reference to this rich body of literature and deeply understanding the relationships between the operational textual entailment definition and relevant linguistic notions is an ongoing research topic beyond the scope of this paper.”
MEBN: A language for first-order Bayesian knowledge bases (2008, background): “Halpern’s [34] logic can express both proportion expressions and degrees of belief, and provides a semantics relating proportions to degrees of belief.”
Statistical Relational Artificial Intelligence: Logic, Probability, and Computation (2016, background): “- Probabilistic logics have been also studied from a knowledge representational perspective [Nilsson, 1986, Halpern, 1990, Poole, 1993b]. e aim of this research was initially more a probabilistic characterization of logic than suitable representations for learning.”