Issues in Temporal and
Causal Inference
Pei Wang
Temple University, USA
Patrick Hammer
Graz University of Technology, Austria
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.
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(E|C)
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 domaindependent
• Causal beliefs are revisable.
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
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
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)
Knowledge Representation
Term names a concept, e.g., bird
Compound Term is composed from other
terms, e.g., ([yellow] ∩ bird)
Inheritance (→) is a relation representing
the substitutability of one term by
another one, e.g.,
{Tweety} → ([yellow] ∩ bird)
$x → raven  $x → [black]
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 = w++wFrequency: f = w+/w
Confidence: c = w / (w +1)
Temporal Knowledge
• An event is a statement whose truthvalue 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]
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
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
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
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