Classification of Entailment Relations in PPDB
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Classification of Entailment Relations in PPDB CHAPTER 5. ENTAILMENT RELATIONS 71 CHAPTER 5. ENTAILMENT RELATIONS 71 R0000 R0001 R0010 R0011 CHAPTER 5. ENTAILMENT RELATIONS CHAPTER 5. ENTAILMENT71 RELATIONS 71 1 Overview equivalence synonym negation antonym R0100 R0101 R0110 R0000R0111 R0001 R0010 R0011 couch able un- This document outlines our protocol for labeling sofa able R0000 R0001 R0010 R0000R0011 R0001 R0010 R0011 R R R R R R R R noun pairs according to the entailment relations pro- 1000 1001 1010 01001011 0101 0110 0111 R R R R R R R R posed by Bill MacCartney in his 2009 thesis on Nat- 0100 0101 0110 01000111 0101 0110 0111 R1100 R1101 R1110 R1000R1111 R1001 R1010 R1011 CHAPTER 5. ENTAILMENT RELATIONS 71 ural Language Inference. Our purpose of doing this forward entailment hyponymy alternation shared hypernym Figure 5.2: The 16 elementary set relations, represented by Johnston diagrams. Each box represents the universe U, and the two circles within the box represent the sets R1000 R1001 R1010 R1000R1011 R1001 R1010 R1011 x and y. A region is white if it is empty, and shaded if it is non-empty. Thus in the carni is to build a labelled data set with which to train a R1100 R1101 R1110 R1111 bird vore CHAPTER 5. ENTAILMENT RELATIONSdiagram labeled R1101,onlytheregionx y is empty,71 indicating that x y U. \ ;⇢ ⇢ ⇢ Figure 5.2: The 16 elementary set relations, represented by Johnston diagrams. Each classifier for differentiating between these relations. R0000 R0001 R0010 R0011 feline box represents the universe U, and the two circles within the box represent the setscanine equivalence classR1100 in which onlyR partition1101 10 is empty.)R1110 These equivalenceR1100R1111 classes areR1101 R1110 R1111 x and y. A region is white if it is empty, and shaded if it is non-empty. Thus in the depicted graphically in figure 5.2. diagram labeledcrow R1101,onlytheregionx y is empty, indicating that x y U. The classifier can be used to assign probabilities of \ ;⇢ ⇢ ⇢ FigureIn fact, 5.2: eachThe 16 of elementarythese equivalence set relations, classes represented is a setFigure relation, by 5.2: Johnston that The is, 16 diagrams.a elementary set of ordered Each set relations, represented by Johnston diagrams.cat Eachdog box represents the universe U, and the two circlesbox within represents the box the represent universe theU, sets and the two circles within the box represent the sets R0000 R0001pairs of sets. WeR0010 will refer to theseR0011 16 set relationsR0100 as the elementaryR0101 set relationsR01,10 R0111 x and y. A region is white if it is empty, and shadedx and if ity is. A non-empty. region is white Thus if in it the is empty, and shaded if it is non-empty. Thus in the each relation to the paraphrase rules in PPDB, mak-and we will denote this set of 16 relations by R.Byconstruction,therelationsinequivalence class in which only partitionR 10 is empty.) These equivalence classes are diagram labeled R1101,onlytheregionx y is empty,diagram indicating labeled thatR1101,onlytheregionx y U. x y is empty, indicating that x y U. \ depicted graphically;⇢ in figure⇢ ⇢ 5.2. \ ;⇢ ⇢ ⇢ are both mutually exhaustivereverse (every entailment ordered pair of setshypernymy belongs to some relation in independence no path ing PPDB a more informative resource for down-R)andmutuallyexclusive(noorderedpairofsetsbelongstotwodiIn fact, each offf theseerent equivalence relations classes is a set relation, that is, a set of ordered R0100 R0101equivalencein R). Thus, class everyR0110 in ordered which only pair partitionR of0111 sets can 10 be is empty.) assignedR1000pairsequivalence These toof exactlysets. equivalence class WeR1001 one in will whichrelation refer classes only to in theseareR partition1.010 16 set 10 relations is empty.)R1011 as These the elementary equivalence set classes relations are, entity stream tasks such as recognizing textual entailmentdepicted graphically in figure 5.2. anddepicted we will graphicallyAsian denote this in figure set of 5.2.16 relations by R.Byconstruction,therelationsinR In fact, each of these equivalence classes is a setare relation,In both fact, mutually that each is, of a exhaustive these set of equivalence ordered (every classesordered is pair a set of relation, sets belongs that to is, some a set relation of ordered in R)andmutuallyexclusive(noorderedpairofsetsbelongstotwodifferent relations (RTE). pairs of sets. We will refer to these 16 set relationspairs as the of sets.elementary We will set refer relations to these, 16 set relations as the elementaryungula set relationssubsta, R R R R te nce 1000 1001and we will denote1010 this set of 161 relations011 by RR.Byconstruction,therelationsin1100inandR we). Thus, will denote everyR1101 thisordered set of pair 16R of1 relations110 sets can by beR assigned.Byconstruction,therelationsinR1111 to exactly one relation in RR. are both mutually exhaustive (every ordered pair ofare sets both belongs mutuallyThai to some exhaustive relation (every in ordered pair of sets belongs to some relation in R)andmutuallyexclusive(noorderedpairofsetsbelongstotwodiFigure 5.2: The 16R elementary)andmutuallyexclusive(noorderedpairofsetsbelongstotwodi set relations,fferent relations represented by Johnston diagrams. Each ffhippoerent relationsfood U in R). Thus, every ordered pair ofbox sets represents can be assigned thein universeR). to Thus, exactly, every and one the ordered relation two circles pair in R of. within sets can the be box assigned represent to exactly the sets one relation in R. R R R Rx and y. A region is white if it is empty, and shaded if it is non-empty. Thus in the 2 Entailment Relations 1100 1101 1110 1111 diagram labeled R1101,onlytheregionx y is empty, indicating that x y U. \ ;⇢ ⇢ ⇢ Figure 5.2: The 16 elementary set relations, represented by Johnston diagrams. Each box represents the universe U, and the two circlesFigure within the box represent2:equivalence Mappings the class sets in which only partition of MacCartney’s 10 is empty.) These equivalence classes relations are onto the x and y. A region is white if it is empty, and shaded if it is non-empty. Thus in the MacCartney’s thesis proposes a method for parti- depicted graphically in figure 5.2. diagram labeled R1101,onlytheregionx y is empty, indicating that x y U. \ Wordnet;⇢ hierarchy.In fact,⇢ each⇢ of these equivalence classes is a set relation, that is, a set of ordered tioning all of the possible relationships that can exist pairs of sets. We will refer to these 16 set relations as the elementary set relations, equivalence class in which only partition 10 is empty.) These equivalenceand we classes will denote are this set of 16 relations by R.Byconstruction,therelationsinR between two phrases into 16 distinctdepicted relationships. graphically in figure 5.2. are both mutually exhaustive (every ordered pair of sets belongs to some relation in In fact, each of these equivalence classes is a set relation, that is,R a)andmutuallyexclusive(noorderedpairofsetsbelongstotwodi set of ordered fferent relations pairs of sets. We will refer to these 16 set relations as the elementaryforwardin R set). Thus,relations every, entailment ordered pair of sets can be (assigned<) to: exactly if one X relation is in trueR. then Y is Of these, he defines the 7 non-degenerateand we will denote relations this set of 16 relations by R.Byconstruction,therelationsinR are both mutually exhaustive (every ordered pair of sets• belongs to some relation in as the “basic entailment relationships.”R)andmutuallyexclusive(noorderedpairofsetsbelongstotwodi MacCart- truefferent but relations if Y is true then X may or may not be in R). Thus, every ordered pair of sets can be assigned to exactly one relation in R. ney’s table explaining these 7 relations is reproduced true. CHAPTER 5. ENTAILMENT RELATIONS 79 in figure 1. reverse entailment (>) : if Y is true then X is • true but if X is true then Y may or may not be symbol10 name example set theoretic definition11 in R x y equivalence couch sofa x = yR1001 true. ⌘ ⌘ x y forward entailment crow bird x yR1101 @ @ ⇢ x y reverse entailment Asian Thai x yR1011 negation ( ) : if X is true then Y is not true and A A ⊃ • ^ x ^ y negation able ^ unable x y = x y = UR0110 \ ;^ [ if Y is not true then X is true, and either X or Y x y alternation cat dog x y = x y = UR1110 | | \ ;^ [ 6 must be true. x y cover animal non-ape x y = x y = UR0111 ` ` \ 6 ;^ [ x # y independence hungry # hippo (all other cases) R1111 alternation ( ) : if X is true then Y is not true The relations in B can be characterized as follows. First, we preserve the semantic • but if Y is notj true then X may or may not be Figurecontainment 1: MacCartney’s relations ( and )ofthemonotonicitycalculus,butfactortheminto 7 basic entailment relations. In v w columnthree mutually 4, U exclusiverefers relations: to the space equivalence of all ( ), phrase (strict) forward pairs entailment(x,y). ( ), true. ⌘ @ and (strict) reverse entailment (A). Second, we include two relations expressing semantic exclusion: negation (^), or exhaustive exclusion, which is analogous to set cover (^) : if X is true then Y may or may not complement;In summary, and alternation the relations ( ), or non-exhaustive are : exclusion. The next relation is • | be true and if Y is true then X may or may not cover (`), or non-exclusive exhaustion. Though its utility is not immediately obvious, be true, and either X or Y must be true. it is theequivalence dual under negation (=) (in : theifX sense is defined true inthen section Y 5.3.1) is true of the and alternation relation.• if Y Finally, is true the independence then X is relation true. (#)coversallothercases:itexpresses independent (#) : if X is true then Y may or non-equivalence, non-containment, non-exclusion, and non-exhaustion. As noted in • section 5.3.2, # is the least informative relation, in that it places the fewest constraints on its arguments.