Montague Meets Markov: Deep Semantics with Probabilistic Logical Form

Second Joint Conference on Lexical and Computational Semantics (*SEM), Volume 1: Proceedings of the Main Conference and the Shared Task, pages 11–21, Atlanta, Georgia, June 13-14, 2013. c⃝2013 Association for Computational Linguistics Montague Meets Markov: Deep Semantics with Probabilistic Logical Form Islam Beltagy§, Cuong Chau§, Gemma Boleda†, Dan Garrette§, Katrin Erk†, Raymond Mooney§ §Department of Computer Science †Department of Linguistics The University of Texas at Austin Austin, Texas 78712 §{beltagy,ckcuong,dhg,mooney}@cs.utexas.edu †gemma.boleda@utcompling.com,katrin.erk@mail.utexas.edu Abstract We combine logical and distributional rep- resentations of natural language meaning by transforming distributional similarity judg- ments into weighted inference rules using Markov Logic Networks (MLNs). We show that this framework supports both judg- ing sentence similarity and recognizing tex- tual entailment by appropriately adapting the MLN implementation of logical connectives. We also show that distributional phrase simi- larity, used as textual inference rules created on the fly, improves its performance. 1 Introduction Tasks in natural language semantics are very diverse and pose different requirements on the underlying formalism for representing meaning. Some tasks require a detailed representation of the structure of complex sentences. Some tasks require the ability to recognize near-paraphrases or degrees of similarity between sentences. Some tasks require logical infer- ence, either exact or approximate. Often it is neces- sary to handle ambiguity and vagueness in meaning. Finally, we frequently want to be able to learn rele- vant knowledge automatically from corpus data. There is no single representation for natural lan- guage meaning at this time that fulfills all require- ments. But there are representations that meet some of the criteria. Logic-based representations (Mon- tague, 1970; Kamp and Reyle, 1993) provide an expressive and flexible formalism to express even complex propositions, and they come with standard- ized inference mechanisms. Distributional mod- hamster( gerbil( sim(# » hamster, # » gerbil) = w 8 x � hamster(x) ! gerbil(x) � | f(w) Figure 1: Turning distributional similarity into a weighted inference rule els (Turney and Pantel, 2010) use contextual sim- ilarity to predict semantic similarity of words and phrases (Landauer and Dumais, 1997; Mitchell and Lapata, 2010), and to model polysemy (Sch¨utze, 1998; Erk and Pad´o, 2008; Thater et al., 2010). This suggests that distributional models and logic- based representations of natural language meaning are complementary in their strengths (Grefenstette and Sadrzadeh, 2011; Garrette et al., 2011), which encourages developing new techniques to combine them. Garrette et al. (2011; 2013) propose a framework for combining logic and distributional models in which logical form is the primary meaning repre- sentation. Distributional similarity between pairs of words is converted into weighted inference rules that are added to the logical form, as illustrated in Fig- ure 1. Finally, Markov Logic Networks (Richardson and Domingos, 2006) (MLNs) are used to perform weighted inference on the resulting knowledge base. However, they only employed single-word distribu- tional similarity rules, and only evaluated on a small 11 set of short, hand-crafted test sentences. In this paper, we extend Garrette et al.’s approach and adapt it to handle two existing semantic tasks: recognizing textual entailment …

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