Semantic Processing Semantic Representation FOPC Inference Issues Description Logics Semantic Processing Semantic Processing Augmenting CFGs Currying Quantifier scope Semantic Grammars L445 / L545 Dept. of Linguistics, Indiana University Spring 2017 1 / 44
Semantic Semantics Processing Semantic Representation FOPC Inference ◮ Semantics = study of meaning Issues Description Logics ◮ We want to investigate the literal meaning of sentences Semantic → compositional semantics Processing ◮ Lexical semantics = study of meaning of words Augmenting CFGs Currying ◮ Word Sense Disambiguation deals with lexical Quantifier scope Semantic Grammars semantics ◮ To represent the meaning of a sentence, we choose First-Order Predicate Calculus (FOPC) & a basic (Davidsonian) event semantics ◮ I have a car ◮ ∃ x , y Having (x) ∧ Haver(Speaker,x) ∧ ThingHad(y,x) ∧ Car(y) 2 / 44
Semantic Part I: Semantic Representation Processing Semantic There are a variety of way to represent semantics, all Representation FOPC sharing some commonalities: Inference Issues Description Logics ◮ Unambiguous representation: the underlying semantic Semantic representation of a sentence should be unambiguous Processing Augmenting CFGs ◮ A sentence might mean multiple things Currying Quantifier scope ◮ But each meaning is represented unambiguously Semantic Grammars ◮ Allows for vagueness : a semantic representation can be partly undefined ◮ I eat Italian food . ◮ Not clear exactly what Italian food refers to. ◮ Verifiable : is a particular sentence true or false? See also Blackburn and Bos (2003), http://www.let.rug.nl/bos/comsem/book1.html 3 / 44
Semantic Canonical Form Processing Semantic Representation FOPC Furthermore, if two distinct sentences mean the same thing, Inference Issues they should have the same semantic representation. Description Logics Semantic ◮ The canonical form is the semantic form for all Processing Augmenting CFGs sentences with the same semantics Currying Quantifier scope Semantic Grammars (1) a. Does Maharani have vegetarian dishes? b. Do they have vegetarian food at Maharani? c. Are vegetarian dishes served at Maharani? d. Does Maharani serve vegetarian food? ◮ All of these sentences should probably have the same representation (for many purposes) 4 / 44
Semantic Model-Theoretic Semantics Processing Semantic Representation Semantic representations are formalized with a model FOPC ◮ A model represents the state of affairs in the world Inference Issues being represented Description Logics Semantic 1. Represent objects, properties of objects, & relations Processing between them Augmenting CFGs Currying 2. Successfully map the meaning representation to the Quantifier scope Semantic Grammars world being considered Meaning representation: ◮ Non-logical vocabulary: names of objects, properties, & relations ◮ Denotation: every element of non-logical vocab corresponds to a fixed, well-defined part of model ◮ Logical vocabulary: closed set of symbols, operators, quanitifers, links, etc.: needed to compose expressions 5 / 44
Semantic Denotation Processing Semantic Representation FOPC Inference Extensional approach to meaning: denotation is reducible Issues Description Logics to sets Semantic Processing ◮ Domain: set of objects/elements that are part of state of Augmenting CFGs Currying affairs Quantifier scope Semantic Grammars ◮ Properties: sets of domain elements which have property in question ◮ Relations: sets of ordered lists/tuples of domain elements Interpretation : Mapping from meaning representations to denotation 6 / 44
Semantic Model of restaurant world Processing Semantic Representation FOPC Inference Issues Description Logics ◮ Domain: D = { a , b , c , d , e , f , g , h , i , j } Semantic ◮ Matthew, Franco, Katie, & Caroline: a , b , c , d Processing Augmenting CFGs ◮ Frasca, Med, Rio: e , f , g Currying Quantifier scope ◮ Properties Semantic Grammars ◮ Frasca, Med, and Rio are noisy: Noisy = { e , f , g } ◮ Relations ◮ Matthew likes the Med. ◮ Katie likes the Med and Rio. ◮ Likes = { < a , f >, < c , f >, < c , g > } 7 / 44
Semantic Predicate-Argument Structure Processing Semantic Representation FOPC Inference Recall verb subcategorization requirement Issues Description Logics Semantic ◮ We can link these syntactic argument slots with Processing semantic roles, or thematic (theta) roles Augmenting CFGs Currying Quantifier scope Syntactic role Semantic role Semantic Grammars Subject NP Agent Object NP Patient ◮ We can further restrict such theta roles to meet certain conditions, so-called selectional restrictions ◮ e.g., the agent role of eat must be an animal 8 / 44
Semantic Towards a Representation Processing Semantic Representation FOPC Inference We can represent verbs with semantic roles by: Issues Description Logics ◮ defining a semantic predicate for that verb (e.g. Eat ) Semantic Processing ◮ giving the predicate the appropriate number of slots Augmenting CFGs Currying (e.g., 2) Quantifier scope Semantic Grammars NP x eats NP y ⇒ Eat ( x , y ) ◮ The slots are filled in by variables (e.g., x , y ), until we can fill them by actual information from a sentence Now to define the structures that are allowed ... 9 / 44
Semantic First-Order Predicate Calculus (FOPC) Processing Semantic Representation Predicates : FOPC Inference Issues ◮ Predicates take arguments & define the relation among Description Logics them, e.g. Eat takes two arguments (eater/eaten) Semantic Processing Augmenting CFGs Terms , or devices to represent objects: Currying Quantifier scope ◮ Constants : specific objects in the world Semantic Grammars e.g., John and fruit in Eat ( John , fruit ) ◮ Variables : like constants, but not totally specified e.g., x in Eat ( John , x ) → : no specification of what John eats ◮ Functions : refer to unique objects which are complex e.g., the restaurant’s location becomes LocationOf ( Restaurant ) 10 / 44
Semantic Why FOPC? Processing Semantic Representation FOPC Inference Issues Description Logics Semantic Processing Advantages of first-order predicate calculus (FOPC): Augmenting CFGs Currying ◮ Proving FOPC statements is efficient Quantifier scope Semantic Grammars ◮ FOPC statements can be linked to syntactic rules ◮ FOPC deals with a wide range of linguistic phenomena 11 / 44
Semantic Logical Connectives Processing Semantic Representation FOPC We can build up predicates and then combine them with Inference Issues logical connectives Description Logics Semantic ◮ not ( ¬ ): I am not happy: ¬ Happy ( Speaker ) Processing Augmenting CFGs ◮ and ( ∧ ): I am happy and free: Currying Quantifier scope Happy ( Speaker ) ∧ Free ( Speaker ) Semantic Grammars ◮ or ( ∨ ): I am happy or I’m free: Happy ( Speaker ) ∨ Free ( Speaker ) ◮ This is an inclusive or : it is true if the speaker is both happy and free (as we’ll see momentarily) ◮ if ( ⇒ ): If I’m free, then I’m happy: Free ( Speaker ) ⇒ Happy ( Speaker ) 12 / 44
Semantic Variables and Quantifiers Processing Semantic Representation FOPC Variables allow a slot to be unfilled, but we need to quantify Inference Issues over (restrict) such variables Description Logics Semantic ◮ ’there exists’ ( ∃ ): a restaurant that serves Mexican food: Processing Augmenting CFGs ∃ xRestaurant ( x ) ∧ Serves ( x , MexicanFood ) Currying Quantifier scope ◮ Substituting a single restaurant which serves Mexican Semantic Grammars food for x will make this logical formula true ◮ ’for all’ ( ∀ ): All vegetarian restaurants serve vegetarian food: ∀ xVegetarianRestaurant ( x ) ⇒ Serves ( x , VegetarianFood ) ◮ For this to be true, all substitutions for x that make VegetarianRestaurant(x) true must also make Serves(x,VegetarianFood) true 13 / 44
Semantic Determining Truth Processing Semantic ◮ Truth-conditional semantics: sentences are analyzed in Representation FOPC terms of whether or not they evaluate to true, with Inference Issues respect to some model Description Logics Semantic To determine whether something is true or not, we evaluate Processing Augmenting CFGs each predicate to see if it’s true, and the connectives are Currying Quantifier scope interpreted as follows (T=True, F=False): Semantic Grammars p q ¬ p p ∧ q p ∨ q p ⇒ q F F T F F T F T T F T T T F F F T F T T F T T T ◮ Possible-worlds semantics: same idea, but true for a given “possible world” 14 / 44
Semantic Rules of Inference Processing Semantic Representation FOPC Inference Issues Rules of inference allow us to draw conclusions based on Description Logics Semantic what information we have Processing ◮ Can add information to database of information Augmenting CFGs Currying Quantifier scope Semantic Grammars Modus ponens : two statements combine to make a third true: ◮ All men are mortal ( ∀ x [ man ( x ) → mortal ( x )] ) ◮ Socrates is a man ( man ( Socrates ) ) ◮ Therefore, Socrates is mortal ( mortal ( Socrates ) ) 15 / 44
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