We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b) measure how strong it is; (c) and do something about it, e.g. suggest ways to reconcile inconsistent advice. This model naturally represents the distinction between contradictions and disagreements. It is based on the idea of representing natural language sentences as formulas with parameters sitting on lattices, creating partial orders based on predicates shared by theories, and building sheaves on these partial orders with products of lattices as stalks. Degrees of disagreement are measured by the existence of global and local sections. Limitations of the sheaf approach and connections to recent work in natural language processing, as well as the topics of contextuality in physics, data fusion, topological data analysis and epistemology are also discussed.
At this point it is not clear to us the relationship of the simple lattice-based inference rule introduced there to the recent work of @cite_15 who is formalizing reasoning with contradictory information withing a framework of sheaves and category theory. To understand both these connections is a topic of our ongoing work.
@cite_15
1515930456 1973673849 2790415926 2166741250
The problem of deciding the satisfiability of a quantifier-free formula with respect to a background theory, also known as Satisfiability Modulo Theories (SMT), is gaining increasing relevance in verification: representation capabilities beyond propositional logic allow for a natural modeling of real-world problems (e.g., pipeline and RTL circuits verification, proof obligations in software systems). In this paper, we focus on the case where the background theory is the combination T1∪T2 of two simpler theories. Many SMT procedures combine a boolean model enumeration with a decision procedure for T1∪T2, where conjunctions of literals can be decided by an integration schema such as Nelson-Oppen, via a structured exchange of interface formulae (e.g., equalities in the case of convex theories, disjunctions of equalities otherwise). We propose a new approach for SMT(T1∪T2), called Delayed Theory Combination, which does not require a decision procedure for T1∪T2, but only individual decision procedures for T1 and T2, which are directly integrated into the boolean model enumerator. This approach is much simpler and natural, allows each of the solvers to be implemented and optimized without taking into account the others, and it nicely encompasses the case of non-convex theories. We show the effectiveness of the approach by a thorough experimental comparison. In the field of infrastructures’ surveillance and protection, it is important to make decisions based on activities occurring in the environment and its local context and conditions. In this paper we use an active rule based event processing architecture in order to make sense of situations from the combination of different signals received by the rule engine. However obtaining some high level information automatically is not without risks, especially in sensitive environments, and detection mistakes can happen for various reasons: the signal’s source can be defective, whether it is human—miss-interpretation of the signal—or computed—material malfunction; the aggregation rules can be wrong syntaxically, for example when a rule will never be triggered or a situation never detected; the interpretation given to the combination of signals does not correspond to the reality on the field—because the knowledge of the rule designer is subjective or because the environment evolves over-time—the rules are therefore incorrect semantically. In this paper, a new approach is proposed to avoid the third kind of error sources. We present a hybrid machine learning technique adapted to the complexity of the rules’ representation, in order to create a system more conform to reality. The proposed approach uses a combination of an Association Rule Mining algorithm and Inductive Logic Programming for rule induction. Empirical studies on simulated datasets demonstrate how our method can contribute to sensible systems such as the security of a public or semi-public place. Large-scale datasets for natural language inference are created by presenting crowd workers with a sentence (premise), and asking them to generate three new sentences (hypotheses) that it entails, contradicts, or is logically neutral with respect to. We show that, in a significant portion of such data, this protocol leaves clues that make it possible to identify the label by looking only at the hypothesis, without observing the premise. Specifically, we show that a simple text categorization model can correctly classify the hypothesis alone in about 67 of SNLI (Bowman et. al, 2015) and 53 of MultiNLI (Williams et. al, 2017). Our analysis reveals that specific linguistic phenomena such as negation and vagueness are highly correlated with certain inference classes. Our findings suggest that the success of natural language inference models to date has been overestimated, and that the task remains a hard open problem. Unifying first-order logic and probability is a long-standing goal of AI, and in recent years many representations combining aspects of the two have been proposed. However, inference in them is generally still at the level of propositional logic, creating all ground atoms and formulas and applying standard probabilistic inference methods to the resulting network. Ideally, inference should be lifted as in first-order logic, handling whole sets of indistinguishable objects together, in time independent of their cardinality. Poole (2003) and (2005, 2006) developed a lifted version of the variable elimination algorithm, but it is extremely complex, generally does not scale to realistic domains, and has only been applied to very small artificial problems. In this paper we propose the first lifted version of a scalable probabilistic inference algorithm, belief propagation (loopy or not). Our approach is based on first constructing a lifted network, where each node represents a set of ground atoms that all pass the same messages during belief propagation. We then run belief propagation on this network. We prove the correctness and optimality of our algorithm. Experiments show that it can greatly reduce the cost of inference.