Issues in Temporal and Causal Inference

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Issues in Temporal and Causal Inference Pei
Wang Temple University, USA Patrick Hammer Graz
University of Technology, Austria
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Predication and Explanation

• Make conclusions about the future and the past
  based on past experience.
• Causal inference Drawing a conclusion about a
  causal connection based on the conditions of the
  occurrence of an effect
• Causal relation Relating a cause event to an
  effect event.

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Classical Causality

• The classical notion of causality is that every
  event E has a unique cause C, which explains why
  E happened, and can predict its happing in the
  future.
• Formal models of causality
• Logical implication, e.g., C ? E
• Conditional probability, e.g., P(EC)

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Limitations of Classical Models

• Insufficient knowledge It is difficult, to find
  the true cause of an event.
• Insufficient resources It is difficult to
  consider all candidate causes.
• The criteria of causality are domain-dependent
• Causal beliefs are revisable.

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NARS as a Reasoning System

• Non-Axiomatic Reasoning System
• a language for representation
• a semantics of the language
• a set of inference rules
• a memory structure
• a control mechanism

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NARS as an AGI System

• Intelligence the capability of a system to
  adapt to its environment and to work with
  insufficient knowledge and resources
• Assumption of Insufficient Knowledge and
  Resources (AIKR)
• To rely on finite processing capacity
• To work in real time
• To be open to unexpected tasks

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Fundamental Issues/Properties
Under AIKR, the system cannot guarantee absolute
correctness or optimality anymore. Validity and
rationality become relative to the available
knowledge and resources. (Related Strive for
simplicity, partial descriptions, coexisting
interpretations, forgetting)
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Knowledge Representation
Term names a concept, e.g., bird Compound Term
is composed from other terms, e.g., (yellow n
bird) Inheritance (?) is a relation representing
the substitutability of one term by another one,
e.g., Tweety ? (yellow n bird) ?x ?
raven? ? ?x ? black?
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Truth-Value Definition
The truth-value of a statement is a pair of
real numbers in 0, 1, and measures the
evidential support to S ? P ?f, c? Total
evidence w ww- Frequency f
w/w Confidence c w / (w 1)
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Temporal Knowledge

• An event is a statement whose truth-value has a
  duration
• A term can name a concept with temporal meaning,
  e.g., today
• A compound term can specify the temporal order
  among components e.g., ?x?leaving? /?
  ?x?gone?

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Temporal Inference
Temporal inference in NARS processes the logical
factor and the temporal factor in
parallel Classical (Pavlovian) conditioning can
be processed as temporal inference
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Classical Conditioning

• The observation of a?c followed by a?u can be
  generalized by induction into ?x?c? /? ?x?u?
• Repeated observations can strengthen the belief
  by increasing its confidence
• New observation of b?c may lead to anticipation
  b?u

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Classical Conditioning (cont.)

• Unrealized anticipation generates negative
  evidence for the belief
• The abduction rule takes the belief and an
  observation of d?u to produce the conclusion that
  d?c may have occurred
• Whenever there are conflicting conclusions, the
  choice rule compares truth-value and simplicity

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Conclusion

• Prediction and explanation can be carried out
  without a well-defined causal relation
• Causal relation is learned, revisable,
  subjective, and domain-dependent
• It is still possible to distinguish causality
  from correlation, enabling condition, and so on