The OpenNARS implementation of the Non-Axiomatic Reasoning System

Context

Learned in this study

Things to explore

Overview

1 Introduction

• NARS has a memory, a logic component and a control component
• The logic component consists of inference rules that work on statements, where the statements are goals, questions and beliefs
  • A statement can be eternal (non time-dependent) or events (time-dependent)
  • Beliefs are statements that the system believes to be true to a certain extent
  • An inference task is a statement to be processed, with additional control relevant information
• NAL: Non-Axiomatic Logic
• Narsese: Language for representing statements

2 Memory

• 3 primary operations:
  • Return the best ranked belief or goal for inference within concepts (local inference)
  • Provide a pair of contextually relevant and semantically related statements for inference between concepts (general inference)
  • Add statements to memory whilst maintaining constraints on the system
• The main loop:
  • Get a concept from memory
  • Get a task and belief related to the selected concept
  • Derive new tasks from the selected task and belief
  • Put the involved items back into the corresponding bags
  • Put the new tasks into the corresponding bags
• System of metadata (budget and stamp)
  • Used to prevent certain forms of invalid inference such as double counting evidence and cyclic reasoning
  • Abstracts temporal requirements away from the Narsese grammar
  • Provides certain implementation efficiencies
• A budget determines the allocation of system resources (time and space) and is defined as $(p, d, q) \in [0, 1] x (0, 1) x [0, 1]$
  • $p$: priority
  • $d$: durability
  • $q$: quality
• A stamp is defined as $(id, t_{cr}, t_{oc}, C, E) \in \mathbb{N} \times \mathbb{N} \times \mathbb{N} \times \mathcal{P}(\mathbb{N})$
  • $id$: unique id
  • $t_{cr}$: creation time
  • $t_{oc}$: occurrence time
  • $C$: syntactic complexity (the number of subterms in the associated term)
  • $E$: an evidential set
• Curve bag is a data structure that supports a probabilistic selection according to the item priority distribution
• The priority value p of the items in the bag maps to their access frequency by a predefined monotonically increasing function
• Called a curve bag because it allows the user to define a custom curve which is highly flexbile and allows emotional parameters and introspective operators to have influence on this selection
• The memory consists of a curve bag of concepts, where a concept is a container for: a concept term, tasklink curve bag, term link curve bag, belief tables and goal tables

Logic Module

• Composed of two components: an inference rule domain specific language (Meta Rule DSL) and an inference rule execution unit
• The Meta Rule DSL != NAL grammar rules
• Meta Rule DSL: provides a flexible methodology to quickly experiment with alternate inference rules, to support the goal of creating a literate program, and to substantially improve the quality of the software implementation
• Meta inference rules take the following form:
  $T, B, P_1, ..., P_n \vdash (C1, ..., C_n)$
  • $T$: the task to be processed
  • $B$: the belief retrieved for the task
  • $P1, ..., P_n$: logical predicates dependent on $T, B, C_1, ..., C_n$
  • $C_1, ..., C_n$: conclusions in the form $(D_i, M_i)$ where $D_i$ is the term of the derived task the conclusion $C_i$ defines, and $M_i$ provides additional meta-information, such as which truth function will be used to decide the truth or desire of the conclusion, how the temporal information will be processed, or whether backwards inference is allowed
• The inference rule execution unit roles are:
  • Parse the Meta Rule DSL into an efficient and executable representation
  • Select and execute the relevant inference rules

4 Temporal Inference Control

• In order to support temporal reasoning, the non-temporal NAL inference rules are extended by adding temporal variants:
  • Temporal window: Events occurring within a specified temporal window will be deemed to have occurred at the same time
  • Temporal chaining: Semantically unrelated events are linked together if they are temporally following one another
  • Interval handling: Events patterns which occur at a given interval from one another can be detected/observed
  • Projection
  • Eternalization
  • Anticipation

5 Projection and Eternalization

• When a truth value for a statement is projected in time, its value decreases according to the following function:
• $c_{new} = (1 - k_c) \times c_{old}$
  • $c_{new}$: new confidence value the belief
  • $c_{old}$: old confidence value the belief
  • $k_c$: confidence decay
• $k_c = \frac{|t_B - t_T|}{|t_B - t_C| + |t_T - t_C|}$
  • $k_c$: confidence decay
  • $t_B$: original occurrence time of the belief
  • $t_T$: projected occurrence time of the belief
  • $t_C$: current time
• In eternalization, the occurrence time is dropped, so the conclusion is about the general situation
• $c_{new} = \frac{1}{k + c_{old}}$
  • $c_{new}$: new confidence value the belief
  • $c_{old}$: old confidence value the belief
  • $k$: a global evidence horizon personality parameter

6 Anticipation

• Based on the observation of an antecedent and behavior, a consequent is excepted (anticipated)
• In the event that an antecedent and behavior is observed, and the consequent is also observed, nothing special needs to be done
• In the opposite case, then the system needs to recognize that the prediction may not be 100% appropriate. Such event will have a high budget and will significantly influence the attention of the system (in order to rectify the situation)

7 Evidence Tracking

• The truth value of a statement is a $(w_+, w_-)$ pair, where $w_+$ represents positive evidence and $w_-$ represents negative evidence
• Can alternatively be represented as a confidence and frequency tuple, where
  • $c = \frac{w_+ + w_-}{k + w_+ + w_-}$
  • $f = \frac{w_+}{w_+ + w_-}$
  • $k$: global personality parameter that indicates a global evidential horizon
• Evidence follows the following principles:
  • Evidence can only be used once for each statement
  • A record of evidence used in each derivation must be maintained, although given AIKR (assumption of insufficient knowledge and resources), this is only a partial record, which is not an issue in practice
  • There can be positive and negative evidence for the same statement
  • Evidence is not only the key factor to determine truth, but also the key to judge the independence of the premises in a step of inference

8 Processing of New and Derived Tasks

• Temporal chaining
• Ranking
• Adding to belief/desire table
• Selecting belief for inference
• Revision
• Decision

9 Attentional Control

• 3 phases process:
  • Select contextually relevant and semantically related tasks for inference
  • Create or update budget values based on user requirements and/or inference results
  • Update memory with results of the updated task and concepts
• Phase 1: Premises for inference are selected according to the following scheme
  • Select a concept from memory
  • Select a tasklink from this concept
  • Select a termlink from this concept
  • Select a belief from the concept the termlink points to ranked by the task
• Phase 2: Formation of new statements (tasks), with new metadata, from the derivations.
• Phase 3: Process the new tasks and insert them into memory.

See also

References

• Paper: The OpenNARS implementation of the Non-Axiomatic Reasoning System (4th Draft for Comment)