complexity and computation - Urbanomic
COMPLEXITY AND COMPUTATION http://thenewcentre.org/seminars/complexity-and-computation-an-introduction-to-measures-paradigms-and-programs/
Case Study
Thinking Complexity
(hierarchies, interaction and structure in Ehresmann-Healy-Ramirez’s category theoretic model of the brain and cognition)
(the necessity of adequate conceptual, logical and mathematical frameworks)
Woodward
Van Fraassen, Kim
Module 1
Rosen, Ehresmann, Healy, Ramirez
Time
(state, regularity, pattern)
Hilb
ert,
Chu
rch , Tu rin
g
Whitehead, Krämer, Novaes ller,
Module 2
gmü , Ste n i lem Vuil
l nte
Pu
(logical vs. causal determinism, artificial vs. natural, object vs. practice, nonreferential sign-design and higher-order abstraction)
Functions, Extensional Objects, Products
Milner, Abramsky
Computability Theory
What is interaction? Why games? (breaking away from intuitive impressions) Wegner, Goldin
Turing (computability by string machines
Locality Boundedness
ge
Church
(effectively calculable function of positive integers ≡ recursive function)
computability by letter machines)
ne
λ-d
ra
efi na b l re =? ility cu rsi ve ne ss
What is computation?
What is computable?
focusing on what computational problems are in general.
focusing on what computable functions are.
Gödel
(general recursiveness for number-theoretic functions) ge
ne
λ-d
efi n l re ≡ abi lit cu rsi y ve ne s
ra
extending Gödel’s critical position s
Kleene
(recusion theory and computable functions)
Multi-agent Problems
(action and knowledge in agent-based modeling, game scenarios, induction puzzles)
Axe
, Re iter,
Computational Hermeneutics of Complex Systems
van Ditm ars
ch
Concurrency Problems
Petri, Dijkstra, Milner
Logical Problems
, ard How , y r ur n, C tze Girard n e G
(theory of processes and resources, scheduling)
Module 3
lrod
(proof theory, syntax-semantics interface, analysis of sequents)
(computational games and strategies, semantics of information processing in asynchronous concurrent systems, interactive logic, etc.) Blass, Abramsky, Japaridze, Jagadeesan
Refinement of Brouwer, Heyting and Kolmogorov’s Constructivist Programs Suspension of structural rules specificaly those involving resources, dualities and symmetries of proof
resource-sensitivity, analysis of actions or abilities, negation as the function of duality or interchange of roles
Developments and Revisions
Languag, Thought and Computation Brandom, Ginzburg, Lecomte, Joinet, van Benthem
bra ,A ss ze a l B Japarid
Logic of computability and re-interpretation of λ-definability
Curien
An
dr eo
li, G
ira
rd
,J
Social Mind and Artificial General Intelligence in the style of multiagent systems
Generalization of the logico-computational concept of game capturing the conservation and transformation of information in asynchronic-concurrent systems, interactive algorithms
ky ms
Girard’s Linear Logic / Geometry of Interaction
Interactive Theory of Computation
oin
Operational semantics of programming languages, re-interpretation of decidability and confluence et
Ludics and study of interactive computational phenomena underlying logical behaviors (connectives and proofs)
Replies to intensional skeptics (“Machines cannot capture intentional mental states.”)
Replies to extensional skeptics (“Machines cannot sufficiently
model extensional behaviors of complex physical systems such as the brain.”)
Case Study
Thinking Complexity
(hierarchies, interaction and structure in Ehresmann-Healy-Ramirez’s category theoretic model of the brain and cognition)
(the necessity of adequate conceptual, logical and mathematical frameworks)
Woodward
Van Fraassen, Kim
Module 1
Rosen, Ehresmann, Healy, Ramirez
Time
(state, regularity, pattern)
Hilb
ert,
Chu
rch , Tu rin
g
Whitehead, Krämer, Novaes ller,
Module 2
gmü , Ste n i lem Vuil
l nte
Pu
(logical vs. causal determinism, artificial vs. natural, object vs. practice, nonreferential sign-design and higher-order abstraction)
Functions, Extensional Objects, Products
Milner, Abramsky
Computability Theory
What is interaction? Why games? (breaking away from intuitive impressions) Wegner, Goldin
Turing (computability by string machines
Locality Boundedness
ge
Church
(effectively calculable function of positive integers ≡ recursive function)
computability by letter machines)
ne
λ-d
ra
efi na b l re =? ility cu rsi ve ne ss
What is computation?
What is computable?
focusing on what computational problems are in general.
focusing on what computable functions are.
Gödel
(general recursiveness for number-theoretic functions) ge
ne
λ-d
efi n l re ≡ abi lit cu rsi y ve ne s
ra
extending Gödel’s critical position s
Kleene
(recusion theory and computable functions)
Multi-agent Problems
(action and knowledge in agent-based modeling, game scenarios, induction puzzles)
Axe
, Re iter,
Computational Hermeneutics of Complex Systems
van Ditm ars
ch
Concurrency Problems
Petri, Dijkstra, Milner
Logical Problems
, ard How , y r ur n, C tze Girard n e G
(theory of processes and resources, scheduling)
Module 3
lrod
(proof theory, syntax-semantics interface, analysis of sequents)
(computational games and strategies, semantics of information processing in asynchronous concurrent systems, interactive logic, etc.) Blass, Abramsky, Japaridze, Jagadeesan
Refinement of Brouwer, Heyting and Kolmogorov’s Constructivist Programs Suspension of structural rules specificaly those involving resources, dualities and symmetries of proof
resource-sensitivity, analysis of actions or abilities, negation as the function of duality or interchange of roles
Developments and Revisions
Languag, Thought and Computation Brandom, Ginzburg, Lecomte, Joinet, van Benthem
bra ,A ss ze a l B Japarid
Logic of computability and re-interpretation of λ-definability
Curien
An
dr eo
li, G
ira
rd
,J
Social Mind and Artificial General Intelligence in the style of multiagent systems
Generalization of the logico-computational concept of game capturing the conservation and transformation of information in asynchronic-concurrent systems, interactive algorithms
ky ms
Girard’s Linear Logic / Geometry of Interaction
Interactive Theory of Computation
oin
Operational semantics of programming languages, re-interpretation of decidability and confluence et
Ludics and study of interactive computational phenomena underlying logical behaviors (connectives and proofs)
Replies to intensional skeptics (“Machines cannot capture intentional mental states.”)
Replies to extensional skeptics (“Machines cannot sufficiently
model extensional behaviors of complex physical systems such as the brain.”)
