Lecture 3 - More logic.docx

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Department
Cognitive Science
Course
COG SCI 190
Professor
Terry Regier
Semester
Fall

Description
 Lecture 3­ More Logic • Truth Tables o Truth of a formula depends on the truth of its parts o An assignment of truth values to propositions (a possible world) that results in a formula  being true is a model of that formula • Limitations of Boole’s Logic: Multiple generality (every v. some) – An affirmation that is both  universal and particular • Frege o Begriffsschrift ­> Concept Script   A formal language that aims to capture the relationships between our thoughts o Modern logic o First­order predicate logic (instead of propositions use predicates to denote properties of  objects)  P(a) like Hairy (Rex) – rex= name of dog o Two new symbols:  Universal Quantifier: Upside down A (for all)   Existential Quantifier: Backwards E (for some, there exists)  Quantifiers: concern variables • All objects or at least one object o  Fixes the problem of Multiple generality (“Everybody loves somebody”)  o CAN’T say “For every property P, there is some object that possesses that property” (that  is second­order logic) • Inference Rule  o X  ▯Y o X o ____ o Y o Modus Ponens (always works no matter what X and Y mean  Synta
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