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Depei Bao's List: Logic

Combinatory logic - Wikipedia, the free encyclopedia

en.wikipedia.org/...Combinatory_logic - Preview

wikipedia on 2008-11-14 and saved by 5 people
- eliminate the need for variables in mathematical logic
- functional programming languages
- 2 more annotations...
- - lambda calculus
  - lambda calculus
Logic and Artificial Intelligence (Stanford Encyclopedia of Philosophy)

plato.stanford.edu/...logic-ai - Preview

Stanford Encyclopedia of Philosophy survey on 2009-01-16 and saved by 6 people
- the Ramification Problem
- the Ramification Problem
- 98 more annotations...
- - the Ramification Problem
  - propositions whose truth values can change
    over time
  - formalizing mathematical domains
  - elaboration tolerance
  - a criterion for the
    adequacy of formalizations
  - an explicit
    ontology
  - explicit
    representations of context
  - simulation techniques
  - see whether
    the goal holds in the plan's final state
  - predictive reasoning
  - the inference of later states from
    earlier ones
  - the dynamics are determined by actions rather than by differential
    equations
  - inferring what does not change
  - Frame Problem
  - formalizing general common sense in arbitrary domains
  - The purely logical Frame
    Problem can be solved using monotonic logic, by simply writing explicit
    axioms stating what does not change when an action is
    performed.
  - situation-dependent
    functions
  - how to
    choose an appropriate set of fluents,
  - treat inertia as a default
  - unless a reason for the change can be found in axioms for
    the action
  - a fluent changes
    truth value a prima facie anomaly
  - The Qualification Problem
  - these exceptions—especially if
    one is willing to entertain far-fetched circumstances—can
    iterate endlessly
  - ceteris paribus generalizations
  - generalizations concerning the consequences of actions
  - circumscriptively
    minimizes preconditions, eliminating from preferred models any “unknown
    preconditions” that might render an action inefficacious
  - The problem is that default logic does not provide for more specific
    defaults to override ones that are more general
  - actions that cannot even be attempted
  - actions that can
    be attempted, but in which the attempt can be expected to go wrong
  - actions
    that can be attempted with reasonable hope of success,
  - actions
    that can be attempted with guaranteed success
  - Obviously, in contemplating a
    plan containing actions that may fail, one may need to reason about the
    consequences of failure
  - the Ramification Problem
  - formalize the indirect consequences of actions
  - inertial defaults will need to be overridden by
    conclusions about ramifications in order to obtain correct results
  - scenarios
  - the Yale Shooting Anomaly
  - the frame default for
    Alive is violated when Fred changes state in the last step
  - if you just go by the number of
    defaults that are violated, both extensions are equally good
  - A plausible, well-motivated logical
    solution to the Frame Problem runs afoul of a simple, crisp example in
    which it clearly delivers the wrong results
  - continuous time, concurrent actions, and various kinds of
    ignorance
  - not only
    prediction and plan verification but retrodiction
  - preference semantics
  - a
    number of temporal logics
  - unmotivated actions are to be minimized
  - an action
    (“actions” construed generally enough to include any change) can be
    motivated directly, e.g. by an axiom, or indirectly, through chains of
    motivations
  - the
    inertial rule CIR is stated using an abnormality
    predicate
  - for
    retrodiction
  - biconditional
  - the Holds predicate is allowed to vary and all
    other parameters are fixed
  - treating uncaused eventualities as
    abnormalities to be minimized
  - causal
    solution to the Yale Shooting Anomaly
  - static laws
  - relate the direct consequences of actions to other changes
  - contraposition of laws
  - purely
    syntactic solution to the Ramification Problem
  - Static laws of the form F→L
  - Dynamic laws of the form A Causes
    L if F
  - the importance of actions and their relation to
    change
  - different kinds of events
    (including structured composite events) in interpreting natural
    language
  - Some of this work is closely
    related to the research in qualitative reasoning
  - Qualitative approaches to space
  - mereology, or qualitative theory of the part-whole
    relation between physical individuals
  - a logical theory of
    relations among regions or the objects that occupy them
  - does not
    depend on construing regions as sets of points
  - Regional Connection Calculus (RCC)
  - a primitive
    C relating regions of space
  - the definability of shapes in RCC
  - More
    recent work based on RCC addresses representation and reasoning about
    motion
  - combines spatial and temporal issues
  - Epistemic logic
  - which constraints are appropriate for knowledge and
    belief
  - formalizing
    knowledge that uses first-order logic
  - a modal language to formalize propositional attitudes
  - hyperintensionality, or closure of epistemic attitudes under
    logical consequence
  - generalized logical foundations
  - introduce multiple agents
  - deontic
    S5 for belief
  - simplify the modality
  - reasoning having to do with agents' attitudes about
    one another's attitudes
  - applications of the logic of
    knowledge
  - the logic of
    perception
  - add sensing actions to the
    repertoire of a planning formalism of the sort
  - overlap with concerns of the
    qualitative physics and qualitative reasoning community
  - Minds and society, however, are new and
    different topics
  - the former has to do with common sense psychology
    and its application in introspective and interpersonal reasoning
  - the latter, of course, should have to do with social and political
    knowledge and reasoning
  - More than half of the book is devoted to reasoning about
    actions and change
  - When larger-scale formalizations are attempted, other
    challenges arise that are similar to those that software engineering
    tries to address
  - suites of “benchmark problems
  - similarities outweigh differences
  - The egg-cracking case raises the problem of how to evaluate
    moderately large formalizations of common sense problems
  - intuitive taxonomic organization of domains
  - taxonomic logics
  - the organization of a
    domain into hierarchies is allowed to have exceptions
  - In the tradition in philosophical logic
  - context is primarily formalized as
    an assignment of values to variables
  - take context
    into account more explicitly

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Updated on 2009-01-16
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Depei Bao's List: Logic

Combinatory logic - Wikipedia, the free encyclopedia

Logic and Artificial Intelligence (Stanford Encyclopedia of Philosophy)

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