Learning entailment rules is fundamental in many semantic-inference applications and has been an active field of research in recent years . In this paper we address the problem of learning transitive graphs that describe entailment rules between predicates ( termed entailment graphs ) . We first identify that entailment graphs exhibit a " tree-like " property and are very similar to a novel type of graph termed forest-reducible graph . We utilize this property to develop an iterative efficient approximation algorithm for learning the graph edges , where each iteration takes linear time . We compare our approximation algorithm to a recently-proposed state-of-the-art exact algorithm and show that it is more efficient and scalable both theoretically and empirically , while its output quality is close to that given by the optimal solution of the exact algorithm . Performing textual inference is in the heart of many semantic inference applications such as Question Answering ( QA ) and Information Extraction ( IE ) . A prominent generic paradigm for textual inference is Textual Entailment ( TUE ) ( Dagan et al . , 2009 ) . In TUE , the goal is to recognize , given two text fragments termed text and hypothesis , whether the hypothesis can be inferred from the text . For example , the text " Cyprus was invaded by the Ottoman Empire in 1571 " implies the hypothesis " The Ottomans attacked Cyprus " . Semantic inference applications such as QA and IE crucially rely on entailment rules ( Ravichandran and Hovy , 2002 ; Shinyama and Sekine , 2006 ) or equivalently inference rules , that is , rules that describe a directional inference relation between two fragments of text . An important type of entailment rule specifies the entailment relation between natural language predicates , e.g. , the entailment rule ' X invade Y → X attack Y ' can be helpful in inferring the aforementioned hypothesis . Consequently , substantial effort has been made to learn such rules ( Lin and Pantel , 2001 ; Sekine , 2005 ; Szpektor and Dagan , 2008 ; Schoenmackers et al . , 2010 ) . Textual entailment is inherently a transitive relation , that is , the rules ' x → y ' and ' y → z ' imply the rule ' x → z ' . Accordingly , Berant et al . ( 2010 ) formulated the problem of learning entailment rules as a graph optimization problem , where nodes are predicates and edges represent entailment rules that respect transitivity . Since finding the optimal set of edges respecting transitivity is NP-hard , they employed Integer Linear Programming ( ILP ) to find the exact solution . Indeed , they showed that applying global transitivity constraints improves rule learning comparing to methods that ignore graph structure . More recently , Berant et al . ( Berant et al . , 2011 ) introduced a more efficient exact algorithm , which decomposes the graph into connected components and then applies an ILP solver over each component . Despite this progress , finding the exact solution remains NP-hard -the authors themselves report they were unable to solve some graphs of rather moderate size and that the coverage of their method is limited . Thus , scaling their algorithm to data sets with tens of thousands of predicates ( e.g. , the extractions of Fader et al . ( 2011 ) ) is unlikely . In this paper we present a novel method for learning the edges of entailment graphs . Our method computes much more efficiently an approximate solution that is empirically almost as good as the exact solution . To that end , we first ( Section 3 ) conjecture and empirically show that entailment graphs exhibit a " tree-like " property , i.e. , that they can be reduced into a structure similar to a directed forest . Then , we present in Section 4 our iterative approximation algorithm , where in each iteration a node is removed and re-attached back to the graph in a locally-optimal way . Combining this scheme with our conjecture about the graph structure enables a linear algorithm for node re-attachment . Section 5 shows empirically that this algorithm is by orders of magnitude faster than the state-of-the-art exact algorithm , and that though an optimal solution is not guaranteed , the area under the precision-recall curve drops by merely a point . To conclude , the contribution of this paper is twofold : First , we define a novel modeling assumption about the tree-like structure of entailment graphs and demonstrate its validity . Second , we exploit this assumption to develop a polynomial approximation algorithm for learning entailment graphs that can scale to much larger graphs than in the past . Finally , we note that learning entailment graphs bears strong similarities to related tasks such as Taxonomy Induction ( Snow et al . , 2006 ) and Ontology induction ( Poon and Domingos , 2010 ) , and thus our approach may improve scalability in these fields as well . Learning large and accurate resources of entailment rules is essential in many semantic inference applications . Employing transitivity has been shown to improve rule learning , but raises issues of efficiency and scalability . The first contribution of this paper is a novel modeling assumption that entailment graphs are very similar to FRGs , which is analyzed and validated empirically . The main contribution of the paper is an efficient polynomial approximation algorithm for learning entailment rules , which is based on this assumption . We demonstrate empirically that our method is by orders of magnitude faster than the state-of-the-art exact algorithm , but still produces an output that is almost as good as the optimal solution . We suggest our method as an important step towards scalable acquisition of precise entailment resources . In future work , we aim to evaluate TNF on large graphs that are automatically generated from huge corpora . This of course requires substantial efforts of pre-processing and test-set annotation . We also plan to examine the benefit of TNF in learning similar structures , e.g. , taxonomies or ontologies .

Challenge: Current inefficient algorithms aim to obtain entailment rules for semantic inference hindering the use of large resources.
Approach: They propose an efficient polynomial approximation algorithm that exploits their observation, entailment graphs have a "tree-like" property.
Outcome: Their iterative algorithm runs by orders of magnitude faster than current exact state-of-the-art solutions while keeping close quality.