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Comment Study the above chain of deduction carefully. Note that each step (apart fromthe introduction of the tautology) is a direct interpretation of a meaningpostulate.We will now get you to construct a similar chain of deduction,reducing a case of anomaly to a basic logical contradiction. (Actually thefollowing exercise on deduction, though we have made it fairly precise andrigorous, is still informal and skirts around several technical problemsinvolving logic and reference.We think it best to avoid these problems in anintroductory text.)Practice Given below are three partial dictionary entries.ABSTRACT: x ABSTRACT 1 ~ x CONCRETEIDEA: x IDEA 1x ABSTRACTSLEEP: x SLEEP 1x CONCRETEWe now give an incomplete chain of deduction reducing the anomaloussentence the idea sleeps to a basic contradiction. Your task is to fill in theomitted stages in the deduction.The idea sleeps(Anomaly)............................................. The idea is an idea(From meaning postulate (Tautology)relating sleep and concrete).....................................................(From meaning postulate relatingidea to abstract).....................................................(From meaning postulate expressingantonymy of abstract and concrete)The idea is concrete and the idea is not concrete(Contradiction of form p & ~p)UNIT 17 Meaning postulates211Feedback The omitted stages are:The idea is abstractThe idea is concrete The idea is not concreteComment So far, all our examples of meaning postulates have involved one-placepredicates. Hyponymy relations between two-place predicates can alsobe expressed by meaning postulates.Example x FATHER y 1x PARENT yComment This is paraphraseable as: If X is Y’s father, then X is Y’s parent.Practice Write meaning postulates to account for the hyponymy between thefollowing pairs of two-place predicates.(1) son, child .........................................................................................(2) kick, strike .........................................................................................(3) hear, perceive .........................................................................................(4) brother, relation .........................................................................................Feedback (1) x SON y 1x CHILD y (2) x KICK y 1x STRIKE y(3) x HEAR y 1x PERCEIVE y (4) x BROTHER y 1x RELATION yComment Cases of binary antonymy between two-place predicates can also be handled.Practice Write meaning postulates, using the negative connective ~ to account for theantonymy between the following pairs:(1) same, different ..............................................................................(2) inside, outside ..............................................................................(3) ignore, pay attention to ..............................................................................(4) friend, enemy ..............................................................................Feedback (1) x SAME y 1~x DIFFERENT y (2) x INSIDE y 1~x OUTSIDE y(3) x IGNORE y 1~x PAY ATTENTION TO y(4) x FRIEND y 1~x ENEMY yComment The converse relationship can also be expressed in terms of meaningpostulates.Practice Write meaning postulates, using 6, to account for the synonymy of thefollowing pairs:(1) own, belong to .......................................................................................(2) above, below .......................................................................................PART FIVE Word meaning212(3) before, after .......................................................................................(4) parent, child .......................................................................................Feedback (1) x OWN y 6 y BELONG TO x (2) x ABOVE y 6 y BELOW x(3) x BEFORE y 6 y AFTER x (4) x PARENT y 6 y CHILD xComment Selectional restrictions apply to two-place predicates. Restrictions may affectthe expression in the ‘subject position’ (the x slot) or the expression in the‘object position’ (the y slot).Example Strike is restricted to concrete objects. John struck the table is fine, but Johnstruck motherhood is not.A meaning postulate to express this fact can be formulated as follows:x STRIKE y 1y CONCRETEPractice Formulate meaning postulates to account for the following selectionalrestrictions:(1) Heat requires a concrete object...........................................................................................................................(2) Nourish requires an animate object...........................................................................................................................Feedback (1) x HEAT y 1y CONCRETE (2) x NOURISH y 1y ANIMATE
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