printer friendly pagePHIL 353A: Proof Theory (MATH 293A)
Gentzen's natural deduction and sequential calculi for first-order propositional and predicate logics. Normalization and cut-elimination procedures. Relationships with computational lambda calculi and automated deduction. Prerequisites: 151, 152, and 161, or equivalents.
PHIL 353B: Proof Theory B
Consistency ordinal as a measure of the strength of a mathematical theory. The open problem of describing the ordinal of mathematical analysis (second order arithmetic). Present state of the problem and approaches to a solution. Prerequisites:
Phil 151,152 or equivalents
| Repeatable
2 times
(up to 6 units total)
PHIL 353C: Functional Interpretations
Finite-type arithmetic. Gödel's functional interpretation and Kreisel's modified realizability. Systems based on classical logic. Spector's extension by bar-recursive functionals. Kohlenbach's monotone interpretation and the bounded functional interpretation. The elimination of weak Kônig's lemma. Uniform boundedness. A look at Tao's hard/soft analysis distinction.
PHIL 355: Logic and Social Choice
Topics in the intersection of social choice theory and formal logic. Voting paradoxes, impossibility theorems and strategic manipulation, logical modeling of voting procedures, preference versus judgment aggregation, role of language in social choice, and metatheory of social choice. May be repeated for credit. Prerequisite: 151 or consent of instructor.
| Repeatable
for credit
PHIL 356: Applications of Modal Logic
Applications of modal logic to knowledge and belief, and actions and norms. Models of belief revision to develop a dynamic doxastic logic. A workable modeling of events and actions to build a dynamic deontic logic on that foundation. (Staff)
PHIL 358: Rational Agency and Intelligent Interaction (CS 222)
For advanced undergraduates, and M.S. and beginning Ph.D. students. Logic-based methods for knowledge representation, information change, and games in artificial intelligence and philosophy. Topics: knowledge, certainty, and belief; time and action; belief dynamics; preference and social choice; games; and desire and intention. Prerequisite: propositional and first-order logic.
PHIL 360: Core Seminar in Philosophy of Science
Limited to first- and second-year Philosophy Ph.D. students.
PHIL 365: Seminar in Philosophy of Science: Time
PHIL 366: Evolution and Communication
Topics include information bottlenecks, signaling networks, information processing, invention of new signals, teamwork, evolution of complex signals, teamwork. Sources include signaling games invented by David Lewis and generalizations thereof, using evolutionary and learning dynamics.
PHIL 370: Core Seminar in Ethics
Limited to first- and second-year students in the Philosophy Ph.D. program.
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