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 domain- dependent 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 + +w - Frequency: f = w + /w Confidence: c = w / (w +1)

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]

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