30,626 research outputs found
An anytime deduction heuristic for first order probabilistic logic
This thesis describes an anytime deduction heuristic to address the decision and optimization form of the First Order Probabilistic Logic problem which was revived by Nilsson in 1986. Reasoning under uncertainty is always an important issue for AI applications, e.g., expert systems, automated theorem-provers, etc. Among the proposed models and methods for dealing with uncertainty, some as, e.g., Nilsson's ones, are based on logic and probability. Nilsson revisited the early works of Boole (1854) and Hailperin (1976) and reformulated them in an AI framework. The decision form of the probabilistic logic problem, also known as PSAT, consists of finding, given a set of logical sentences together with their probability value to be true, whether the set of sentences and their probability value is consistent. In the optimization form, assuming that a system of probabilistic formulas is already consistent, the problem is: Given an additional sentence, find the tightest possible probability bounds such that the overall system remains consistent with that additional sentence. Solution schemes, both heuristic and exact, have been proposed within the propositional framework. Even though first order logic is more expressive than the propositional one, more works have been published in the propositional framework. The main objective of this thesis is to propose a solution scheme based on a heuristic approach, i.e., an anytime deduction technique, for the decision and optimization form of first order probabilistic logic problem. Jaumard et al. [33] proposed an anytime deduction algorithm for the propositional probabilistic logic which we extended to the first order context
Anytime Computation of Cautious Consequences in Answer Set Programming
Query answering in Answer Set Programming (ASP) is usually solved by
computing (a subset of) the cautious consequences of a logic program. This task
is computationally very hard, and there are programs for which computing
cautious consequences is not viable in reasonable time. However, current ASP
solvers produce the (whole) set of cautious consequences only at the end of
their computation. This paper reports on strategies for computing cautious
consequences, also introducing anytime algorithms able to produce sound answers
during the computation.Comment: To appear in Theory and Practice of Logic Programmin
Heuristic Ranking in Tightly Coupled Probabilistic Description Logics
The Semantic Web effort has steadily been gaining traction in the recent
years. In particular,Web search companies are recently realizing that their
products need to evolve towards having richer semantic search capabilities.
Description logics (DLs) have been adopted as the formal underpinnings for
Semantic Web languages used in describing ontologies. Reasoning under
uncertainty has recently taken a leading role in this arena, given the nature
of data found on theWeb. In this paper, we present a probabilistic extension of
the DL EL++ (which underlies the OWL2 EL profile) using Markov logic networks
(MLNs) as probabilistic semantics. This extension is tightly coupled, meaning
that probabilistic annotations in formulas can refer to objects in the
ontology. We show that, even though the tightly coupled nature of our language
means that many basic operations are data-intractable, we can leverage a
sublanguage of MLNs that allows to rank the atomic consequences of an ontology
relative to their probability values (called ranking queries) even when these
values are not fully computed. We present an anytime algorithm to answer
ranking queries, and provide an upper bound on the error that it incurs, as
well as a criterion to decide when results are guaranteed to be correct.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
Ancestral Causal Inference
Constraint-based causal discovery from limited data is a notoriously
difficult challenge due to the many borderline independence test decisions.
Several approaches to improve the reliability of the predictions by exploiting
redundancy in the independence information have been proposed recently. Though
promising, existing approaches can still be greatly improved in terms of
accuracy and scalability. We present a novel method that reduces the
combinatorial explosion of the search space by using a more coarse-grained
representation of causal information, drastically reducing computation time.
Additionally, we propose a method to score causal predictions based on their
confidence. Crucially, our implementation also allows one to easily combine
observational and interventional data and to incorporate various types of
available background knowledge. We prove soundness and asymptotic consistency
of our method and demonstrate that it can outperform the state-of-the-art on
synthetic data, achieving a speedup of several orders of magnitude. We
illustrate its practical feasibility by applying it on a challenging protein
data set.Comment: In Proceedings of Advances in Neural Information Processing Systems
29 (NIPS 2016
Renormalization and Computation II: Time Cut-off and the Halting Problem
This is the second installment to the project initiated in [Ma3]. In the
first Part, I argued that both philosophy and technique of the perturbative
renormalization in quantum field theory could be meaningfully transplanted to
the theory of computation, and sketched several contexts supporting this view.
In this second part, I address some of the issues raised in [Ma3] and provide
their development in three contexts: a categorification of the algorithmic
computations; time cut--off and Anytime Algorithms; and finally, a Hopf algebra
renormalization of the Halting Problem.Comment: 28 page
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