Lecture 11: SemanticsProfessor Robert C. [email protected]/9.611J SP11The Menu Bar• Administrivia: Lab 4 out• What knowledge do we need beyond syntax?• How should we represent this?• How can we learn it?6.863J/9.611J SP11Programming Language Interpreter• What is the meaning of 3+5*6?• First parse it into 3+(5*6)+3*56EEFEEE3FN5N6N*+6.863J/9.611J SP11Programming Language Interpreter• What is meaning of 3+5*6?• First parse it into 3+(5*6)• Now give a meaning toeach node in the tree(bottom-up)+3*56EEFEEE3FN5N6N*+35 6303335 63033addmult6.863J/9.611J SP11Interpreting in an Environment• How about 3+5*x?• Same thing: the meaningof x is found from theenvironment (it’s 6)• Analogies in language?+3*5x35 63033EEFEEE3FN5N6N*+35 63033addmult6.863J/9.611J SP11Compiling• How about 3+5*x?• Don’t know x at compile time• “Meaning” at a nodeis a piece of code, not anumberEEFEEE3FN5NxN*+35 xmult(5,x)add(3,mult(5,x))addmult5*(x+1)-2 is a different expression that produces equivalent code (can be converted to the previous code by optimization)Analogies in language?6.863J/9.611J SP11What Counts as Understanding?some notions• We understand if we can respond appropriately• ok for commands, questions (these demand response)• “Computer, warp speed 5”• “throw axe at dwarf”• “put all of my blocks in the red box”• imperative programming languages• database queries and other questions• We understand a statement if we can determine its truth• ok, but if you knew whether it was true, why did anyonebother telling it to you?• comparable notion for understanding a noun phrase is tocompute what the noun phrase refers to, which might beuseful6.863J/9.611J SP11What Counts as Understanding?some notions• We understand statement if we know how to determine its truth• What are exact conditions under which it would be true?• necessary + sufficient• Equivalently, derive all its consequences• what else must be true if we accept the statement?• Philosophers tend to use this definition• We understand statement if we can use it to answer questions [verysimilar to above – requires reasoning]• Easy: John ate pizza. What was eaten by John?• Hard: White’s first move is P-Q4. Can Black checkmate?• Constructing a procedure to get the answer is enough6.863J/9.611J SP11What Counts as Understanding?some notions• Be able to translate• Depends on target language• English to English? bah humbug!• English to French? reasonable• English to Chinese? requires deeper understanding?• English to logic? deepest – the definition we’ll use!• all humans are mortal = ∀x [human(x) ⇒mortal(x)]• Assume we have logic-manipulating rules to tell us how to act,draw conclusions, answer questions …6.863J/9.611J SP11Plan• First:• Let’s look at some sentences and phrases• What would be reasonable logical representations forthem?• Then:• How can we build those representations?• Another course (AI):• How can we reason with those representations?6.863J/9.611J SP11Where we stand: How can a computer‘understand’ a discourse?Here’s a “discourse”. Let’s see how to chop it up….Dolphins are mammals, not fish. They are warm blooded likeman, and give birth to one baby called a calf at a time. Atbirth a bottlenose dolphin calf is about 90-130 cms longand will grow to approx. 4 meters, living up to 40years.They are highly sociable animals, living in podswhich are fairly fluid, with dolphins from other podsinteracting with each other from time to time.6.863J/9.611J SP11At least three parts to ‘semantics’1. Lexical semantics2. Logical semantics3. Discourse semantics6.863J/9.611J SP11Lexical semantics: nouns & verbsDolphins are mammals, not fish. They are warmblooded like man, and give birth to one babycalled a calf at a time. At birth a bottlenosedolphin calf is about 90-130 cms long and willgrow to approx. 4 meters, living up to 40years.They are highly sociable animals, living inpods which are fairly fluid, with dolphins fromother pods interacting with each other from timeto time.6.863J/9.611J SP11Word meanings? Try WordNet• We’ll have a LOT more to say about this later…but for now…6.863J/9.611J SP11What about 90, pods, ?6.863J/9.611J SP11Logical semantics: everything becomes afirst-order logical operatorDolphins are mammals, not fish. They are warmblooded like man, and give birth to one babycalled a calf at a time. At birth a bottlenosedolphin calf is about 90-130 cms long and willgrow to approx. 4 meters, living up to 40years.They are highly sociable animals, living inpods which are fairly fluid, with dolphins fromother pods interacting with each other from timeto time.6.863J/9.611J SP11Discourse semantics: words that tiesentences together (pronouns,‘anaphora’)Dolphins are mammals, not fish. They are warmblooded like man, and give birth to one babycalled a calf at a time. At birth a bottlenosedolphin calf is about 90-130 cms long and willgrow to approx. 4 meters, living up to 40years.They are highly sociable animals, living inpods which are fairly fluid, with dolphins fromother pods interacting with each other from timeto time.Question: what words have we missed?6.863J/9.611J SP11What words are left out so far?Dolphins are mammals, not fish. They are warmblooded like man, and give birth to one babycalled a calf at a time. At birth a bottlenosedolphin calf is about 90-130 cms long and willgrow to approx. 4 meters, living up to 40years.They are highly sociable animals, living inpods which are fairly fluid, with dolphins fromother pods interacting with each other from timeto time.Some of these are obviously ‘logical’…6.863J/9.611J SP11What are we left with?Dolphins are mammals, not fish. They are warmblooded like man, and give birth to one babycalled a calf at a time. At birth a bottlenosedolphin calf is about 90-130 cms long and willgrow to approx. 4 meters, living up to 40years.They are highly sociable animals, living inpods which are fairly fluid, with dolphins fromother pods interacting with each other from timeto time.Red items = in wordnet, but need translation to logic;Blue items = require logical translation ‘from time to time’Today, we’ll focus on the logical semantics6.863J/9.611J SP11Logical semantics: everything thatbecomes a first-order logical operator,including quantifiersDolphins are mammals, not fish. They are warmblooded like man, and give birth to one
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