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Quantifiers in Predicate Logic HG2002 Semantics and Pragmatics Semantics and Pragmatics Review Francis Bond Division of Linguistics and Multilingual Studies http://www3.ntu.edu.sg/home/fcbond/ [email protected] Lecture 12 Location: HSS Auditorium Creative Commons Attribution License: you are free to share and adapt as long as you give appropriate credit and add no additional restrictions: https://creativecommons.org/licenses/by/4.0/. HG2002 (2018) Review Overview ã Overall Review ã Review of the lectures ã Parting Words Final in class quiz Same time and place, next week HG2002 (2018) 1 Big Picture ã Language can be used to convey information ­ we model this as meaning ­ lexical semantics looks at relations between words in the lexicon ­ structural semantics looks at relations between words in utterances ­ pragmatics looks at how and why we use words ã Meaning is infinite ­ it can be built up compositionally ­ it can vary and be extended continuously ­ we can only model it approximately HG2002 (2018) 2 Revision: Introduction to Semantics HG2002 (2018) 3 What is Semantics ã Very broadly, semantics is the study of meaning ­ Word meaning ­ Sentence meaning ã Layers of Linguistic Analysis 1. Phonetics & Phonology 2. Morphology 3. Syntax 4. Semantics 5. Pragmatics ã Semantics could be autonomous or integrated with other knowledge HG2002 (2018) 4 Meaning in the larger context ã Semiotics is the study of interpreting symbols, or signification ­ We refer to the signified ­ Using a signifier Saussure ã Problems with defining meaning ­ The grounding problem and circularity ­ The boundaries of meaning: linguistic vs encyclopedic knowledge ­ Individual variation in meaning: idiolects ­ Words can be combined to form an infinite number of expres- sions ∗ This building up of meaning is referred to as composition ∗ If the meaning of the whole can be deduced from the parts then it is compositional HG2002 (2018) 5 Metalanguages and Notational Conventions We use language to talk about language, which can get messy. So we use certain words with very specific technical senses, and we use fonts to convey information. ã word “gloss” or utterance (do this in your assignments!) ã lexeme ã predicate ã concept ã technical term remember me! HG2002 (2018) 6 Utterances, Sentences and Propositions ã utterance: an actual instance of saying (or writing or …) some- thing ã sentence: an abstraction, the type of what was said (1) Caesar invades Gaul ã proposition: a further abstraction, normally ignoring some non-literal meaning (2) invade(Caesar, Gaul) ­ information structure: what part of a proposition is empha- sized (3) Caesar invaded Gaul (4) Gaul was invaded by Caesar HG2002 (2018) 7 (5) It was Gaul that Caesar invaded (6) It was Caesar who invaded Gaul HG2002 (2018) 8 Information Theory ã Language has many uses, only one of which is to convey infor- mation — but surely transferring information is important ã We can measure information in a limited, technical, and very useful, sense ­ Think of a signal being transmitted from a source to a des- tination, possibly with noise in the channel ­ Measure information in bits: the number of yes/no questions needed to determine a term ­ Context can help decoding due to Mutual Information ã How can we get our message across efficiently and safely ­ Optimal encoding can make the transmission efficient Frequent expressions should be short not in Saeed 9 ­ Redundant encoding can make the transmission robust So we can understand even with noise not in Saeed 10 Revision: Meaning, Thought and Reality HG2002 (2018) 11 Referential View Speaker Refer Say Expression Referent Denote Referential view is focused on direct relationships between expressions (words, sentences) and things in the world (realist view). (More in Chapter 10) HG2002 (2018) 12 Representational View Refer Concept Speaker Denote Represent Say Expression Referent Representational view is focused on how relationships be- tween expressions (words, sentences) and things in the world are mediated by the mind (cognitive linguistics). (More in Chapters 9 and 11) HG2002 (2018) 13 Two types of naming ã The description theory: Names are like short hands for de- scriptions: William Shakespeare = “the playwright who wrote Hamlet” ã The causal theory: Names begin with some event of naming (e.g. a christening) before becoming commonly accepted. William Shakespeare = “the guy other people call William Shakespeare” HG2002 (2018) 14 Mental Representations ã Divide meaning into ­ reference: the relation to the world ­ sense: the rest of the meaning ã Introduce concepts ­ Classic view is to represent by Necessary and Sufficient Conditions: definitional view of meaning bachelor is an unmarried male adult. HG2002 (2018) 15 Prototype Theory ã Some members of a category are more typical and more salient than other members of the same category. (Rosch) ­ Membership is not just IN/OUT but graded ­ Members may share some attributes but not all ­ Categories are culture dependant ­ Concepts are organized in groups around a prototype ­ These have typical members (remembered as exemplars) ­ prototypes have characteristic features ­ Some categories (concepts) are seem to be more psycho- logically basic than others: basic level categories ∗ You only need to store detailed knowledge about BLCs ∗ Other things are then compared to them ∗ Makes it quicker and easier to compute similarities and dif- ferences HG2002 (2018) 16 Basic Level Categories ã Some categories (concepts) are more basic than others ­ maximize the number of attributes shared by members of the category ­ minimize the number of attributes shared with other cate- gories ã They have various properties ­ Pictures of objects are categorized faster at the basic level ­ Basic level names used more often in free-naming tasks ­ Children learn them earlier ­ Basic-level names are more common in adult discourse ­ Basic-level categories are common in different cultures ­ Basic level names tend to be short ­ Basic-level names tend to be common in compound nouns HG2002 (2018) 17 Linguistic Relativity ã The language we think in makes some concepts easy to ex- press, and some concepts hard ã The idea behind linguistic relativity is that this will effect how you think ã Do we really think in language? ­ We can think of things we don’t have words for ­ Language under-specifies meaning ã Maybe we store a more abstract representation the language of thought or Mentalese HG2002 (2018) 18 Revision: Word Meaning HG2002 (2018) 19 Words word slippery to define: orthographic, phonological, conceptual definitions mainly overlap lexeme base (uninflected) form of a word (or multi word expres- sion) vagueness having an underspecified meaning ambiguous having more than one possible meaning content word with a denotation (typically open class : lexical word) function word no denotation (typically closed class: grammat- ical word, structural word) We saw issues with MWEs in the assignment 20 Senses and Relations polysemous having multiple meanings ã this implies that words are somehow divided into senses ã presumably we remember them: so we have an inventory ã if there is no mechanism for extension then this is a fixed sense inventory ã how we generate meaning dynamically is a hot research topic monosemous having just one meaning homonyms words unrelated meaning; grammatically equiva- lent; with identical forms HG2002 (2018) 21 Lexical Relations synonymy all meanings identical; in all contexts; descriptive and non- hyponymy is-a, kind-of: supertype hypernym; subtype hy- ponym meronymy part-whole: part meronym; whole holonym antonymy (complementary, gradable, reverse, converse, taxo- nomic sisters) member-collection member of a group (tree-forest) portion-mass element of stuff (grain-rice) domain used in a domain ([software] driver -golf) HG2002 (2018) 22 Revision: Sentence Relations and Truth HG2002 (2018) 23 Logic ã Classical logic is an attempt to find valid principles of argument and inference. a If something is human then it is mortal premise b Socrates is human premise c Socrates is mortal conclusion ã Can we go from a and b to c? Yes ã Truth is empirical: The premises need to correspond with the facts of the world ­ Sentences have truth values (true, false or unknown) ­ The state of the world that makes a sentence true or false are its truth conditions HG2002 (2018) 24 Methods of Argument ã Modus Ponens a If something is human then it is mortal b Socrates is human c Socrates is mortal p ! q; p ` q ã Modus tollens a If something is human then it is mortal b Zeus is not mortal c Zeus is not human p ! q; :q ` :p HG2002 (2018) 25 ã Hypothetical syllogism a If something is human then it is mortal b If something is mortal then it dies c If something is human then it dies p ! q; q ! r ` p ! r ã Disjunctive syllogism (modus tollendo ponens: affirm by denying) a Either a human is mortal or a human is immortal b A human is not immortal c A human is mortal p _ q; :q ` p (also true that :p ` q) p ⊕ q; :q ` p (also true that :p ` q) p ⊕ q; q ` :p (also true that p ` :q) HG2002 (2018) 26 Empirical truths and connectives p q p ! q p ^ q p _ q p ⊕ q p ≡ q :p if and or XOR iff not T T T T T F T F T F F F T T F F F T T F T T F T F F T F F F T T ã Words themselves often carry more implications I did A and B often implies I did A first ã There are many ways of saying the operations HG2002 (2018) 27 Necessary Truth, A Priori Truth and Analyticity ã Arguments from the speaker’s knowledge ­ A priori truth is truth that is known without experience. ­ A posteri truth is truth known from empirical testing. ã Arguments from the facts of the world ­ Necessary truth is truth that cannot be denied without forc- ing a contradiction.
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