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‘OpenNARS for Applications’: Architecture and
Control
Patrick Hammer1and Tony Lofthouse2
1Department of Computer & Information Sciences
College of Science and Technology
Temple University
Philadelphia PA 19122, USA
patrick.hammer@temple.edu
2Reasoning Systems Ltd (UK)
Tony.Lofthouse@Reasoning.Systems
Abstract. A pragmatic design for a general purpose reasoner incorpo-
rating the Non-Axiomatic Logic (NAL) and Non-Axiomatic Reasoning
System (NARS) theory. The architecture and attentional control differ
in many respects to the OpenNARS implementation. Key changes in-
clude; an event driven control process, separation of sensorimotor from
semantic inference and a different handling of resource constraints.
Keywords: Non-Axiomatic Reasoning ·Sensorimotor ·Artificial Gen-
eral Intelligence ·General Machine Intelligence ·Procedure Learning ·
Autonomous Agent ·Inference Control ·Attention
1 Introduction
The Non-Axiomatic Reasoning System has been implemented several times ([10],
[9], [6]). OpenNARS was used both as a platform for new research topics and an
implementation for applications [5], though it was mainly intended as a research
platform. Not all ideas in OpenNARS are complete, and application domains
require the proven aspects to work reliably. Whilst this has led to the systems
capabilities being stretched to the limits it has also given us a better under-
standing of the current limitations. The proposed architecture, OpenNARS for
Applications (ONA), has been developed to resolve OpenNARS’s limitations by
combining the best results from our research projects. The logic and conceptual
ideas of OpenNARS [6], the sensorimotor capabilities of ANSNA [7] and the con-
trol model from ALANN [9] are combined in a general purpose reasoner ready
to be applied.
ONA is a NARS as described by Non-Axiomatic Reasoning System theory
[18]. For a system to be classified as an instance of a NARS it needs to work under
the Assumption of Insufficient Knowledge and Resource (AIKR). This means the
system is always open to new tasks, works under finite resource constraints, and
works in real time. For the resource constraints to be respected, each inference
step (cycle) must take an approximately constant time O(1), and forgetting is
2 P. Hammer, T. Lofthouse
necessary to stay within memory limits. Here, relative forgetting describes the
relative ranking of items for priority based selection (a form of attention), while
absolute forgetting is a form of eviction of data items, to meet space constraints.
Events, beliefs and concepts compete for resource based on current importance,
relevance and long term usefulness.
What all Non-Axiomatic Reasoning Systems have in common is the use of the
Non-Axiomatic Logic (NAL) [18], a term logic with evidence based truth values,
which allows the systems to deal with uncertainty. Due to the compositional
nature of NAL, these systems usually have a concept centric memory structure,
which exploits subterm relationships for control purposes. A concept centric
memory structure ensures premises in inference will be semantically related. This
property, together with the priority based selection, helps to avoid combinatorial
explosion. An additional commonality between NARS implementations is the
usage of the formal language Narsese, it allows the encoding and communication
of NAL sentences with the system, as well as between systems.
Compared to BDI models [1] [3], plans and intentions are treated as beliefs,
as procedure knowledge is learnable by NARS, instead of being provided by the
user. Just selecting a plan according to desires / goals to become an intention,
based on current circumstances (beliefs), is a much simpler problem to solve, as
it ignores the learning aspect of behaviors which is so critical for AGI. Reinforce-
ment learning (see [15], [19] and [14]) captures the learning aspect and solves
the Temporal Credit Assignment Problem, but does so just for a single signal
(reward, a single outcome). NARS solves it for all events it can predict, some
of which may correspond to goals to achieve. There is also multi objective rein-
forcement learning [8] [16], which however does not capture a changing utility
function corresponding to changing goals. NARS does not learn a fixed state-
action mapping, but instead its behaviors can change rapidly with the changing
goals. Hence, NARS combines and extends the key aspects of both BDI and
Reinforcement Learning without inheriting some of their limitations.
2 Data Structures
Data structures can be grouped into two broad classes: Data and contain-
ers. The primary data elements are Events, Concepts, Implications and Terms;
whilst the containers are FIFO, PriorityQueue, ImplicationTable and HashTable.
HashTable is an optimisation and mentioned here for completeness but is not
required for the functional description. It is used to efficiently retrieve a concept
by its term (hash key) without searching through memory.
Term: All knowledge within the reasoner is represented as a term. Their
structure is represented via a binary tree, where each node can either be a
logical NAL copula or atomic.
Event: Each Event consists of a term with a NAL Truth Value, a stamp
(a set of IDs representing, the evidential base of any derivations or a single ID
for new input), an Occurrence Time, and a priority value. The stamp is used to
‘OpenNARS for Applications’: Architecture and Control 3
check for statistical independence of the premises, derivations are only allowed
when there is no overlap between the stamps of the premises.
Concept: Each concept has a term (its identifier), a priority value for atten-
tion control purposes, a usage value, indicating when the concept was last used
and how often it was used since its creation. There is a table of pre-condition
implications that act as predictive links, specifying which concepts predict which
other’s events. Plus an eternal belief (giving a summary of event truths), most
recent event belief, and predicted event belief.
Implication: These are the contents of the pre-condition implication tables
in the concepts. Usually its term has the form a⇒bwhich stands for “a predicts
b”. Sometimes they also include an operation, such as (a, op)⇒b, which is
the procedural form, and similar to schemas as in [2], though their context is
never modified. They allow the reasoner to predict outcomes (forward) and to
predict subgoals (backward). When the outcome bis predicted (with an operation
execution as side effect for the procedural form), negative evidence is added
to the prediction on failure, while on success positive evidence is added. The
simplest way to accomplish this is to add the negative evidence right away while
ensuring that the positive evidence added will outweigh the negative. In this way
no anticipation deadline needs to be assumed and the truth expectation of the
implication will gain truth expectation on success, and loose truth expectation
on failure, anticipation realized via Assumption of Failure.
PriorityQueue: This is used by: Cycling Events Queue and Concepts Mem-
ory. It is a ranked, bounded priority queue which, when at capacity, removes the
lowest ranked item when a new item is added. Events are ranked by priority, and
concepts by usefulness, a (lastU sed, useCount) which maps to raw usefulness
via usefulnessRaw =useC ount
recency+1 , where recency =cur rentT ime −lastU sed. A
normalised value for usefulness is obtained with usefulness =usef ulnessRaw
usefulnessRaw+1 .
Implication Table and Revision: Implications are eternal beliefs of the
form a⇒b, which essentially becomes a predictive link for a, which is added
into an implication table (precondition implication table of b).
An implication table combines different implications, for instance a⇒g
and b⇒gto describe the different preconditions which lead to g, stored in
the implication table in concept g. Implication tables are ranked by the truth
expectations of the beliefs, where exp(f , c) is defined as (c∗(f−1
2) + 1
2), the
confidence as c=w
w+1 where w=w++w−is the total evidence, w+and w−the
positive and negative evidence respectively, and frequency is defined as f=w+
w.
3 Architecture
A key driver of the architectural change is the nature of how concept, task and
belief are selected for inference. In OpenNARS the selection is based on a prob-
abilistic choice from a data structure (Bag) and is concept centric [13]. ONA
takes a different approach: an event is popped from a bounded priority queue.
The event determines the concept to be selected, through a one-to-one map-
ping between event and concept terms. Then a subset of concepts are selected
4 P. Hammer, T. Lofthouse
based on their priority (determined by a configuration parameter). This selec-
tion of concepts is the attentional focus as these are the concepts that will be
involved in the inference cycle. Whilst the number of concepts to select is a fixed
value (for a given configuration), the priority of concepts is constantly changing.
A self-regulating threshold is used to maintain the priority distribution within
the necessary range to meet the selection criteria. This selection of concepts is
the first stage of the inference cycle. The selected concepts are now tested for
evidential overlap between the event and concept beliefs (evidence cannot be
overlapping [6]). Finally, there is an ‘inference pattern’ match check, between
the event and belief. If all the conditions are met the inference result is gener-
ated, and added to memory to form new concepts or to revise any pre-existing
concept’s belief. Then the event, or the revised one if revision occurred, is re-
turned to the cycling events queue, with a reduced priority (if above minimum
parameter thresholds).
Fig. 1: High level architecture showing input sequencing and cycles for sensori-
motor and semantic inference
Sensory Channels: The reasoner allows for sensory input from multiple
modalities. Each sensory channel essentially converts sensory signals to Narsese.
Dependent on the nature of the modality, its internals may vary. As an example
for application purposes, a Vision Channel could consist of a Multi-Class Multi-
Object Tracker for the detection and tracking of instances and their type, and
an encoder which converts the output into: the instances which were detected
‘OpenNARS for Applications’: Architecture and Control 5
in the current moment, their type, visual properties, and spatial relationships
among the instances [5].
FIFO Sequencer: The Sequencer is responsible for multi-modal integration.
It creates spatio-temporal patterns (compound events) from the events gener-
ated by the sensory channels. It achieves this by building both sequences and
parallel conjunctions, dependent on their temporal order and distance. These
compositions will then be usable by sensorimotor inference (after concepts for
the sequence have been added to concept memory and the compound event
added as belief event within the concept). As shown in figure 1, these compound
events go through cycling events first, ideally to compete for attention with
derived events to be added to memory. The resource allocation between input
and derivations is a difficult balance, for now, we let input events and the com-
pound events (from FIFO sequencer) be passed to memory before derivations.
We acknowledge that this simple solution might not be the final story.
Cycling Events queue: This is the global attention buffer of the reasoner.
It maintains a fixed capacity: items are ranked according to priority, and when
a new item enters, the lowest priority item is evicted. For selection, the highest-
priority items are retrieved, both for semantic and sensorimotor inference, the
retrieved items and the inference results then go back into the cycling events
queue after the corresponding inference block. The item’s priority decays on
usage, but also decays in the queue, both decay rates are global parameters.
Sensorimotor Inference: This is where temporal and procedural reason-
ing occurs, using NAL layers 6-8. The responsibilities here include: Formation
and strengthening of implication links between concepts, driven both by input
sequences and derived events. Prediction of new events based on input and de-
rived events, via implication links. Efficient subgoaling via implication links and
decision execution when an operation subgoal exceeds decision threshold [4].
Semantic Inference: All declarative reasoning using NAL layers 1-6 occurs
here as described in [18], meaning no temporal and procedural aspects are pro-
cessed here. As inheritance can be seen as a way to describe objects in a universe
of discourse [17], the related inference helps the reasoner to categorize events, and
to refine these categorizations with further experience. Ultimately this allows the
reasoner to learn and use arbitrary relations, to interpret situations in richer ways
and find crucial commonalities and differences between various knowledge. Also,
due to the descriptive power of NAL and its experience-grounded semantics,
semi-natural communication with the reasoner becomes possible, and high-level
knowledge can be directly communicated. This also works when the meaning of
some terms is not yet clear and needs to be enriched to become useful.
Concept Memory: The concept store of the reasoner. Similar to the cy-
cling events queue, it maintains a fixed capacity: but instead of being ranked by
priority, items are ranked according to usefulness, and when a new item enters,
the lowest useful item is evicted. Usefulness takes both the usage count and last
usage time into account, to both, capture the long term quality of the item, and
to give new items a chance. All events from the cycling events queue, both input
and derived, that weren’t evicted from the queue, arrive here. A concept node is
6 P. Hammer, T. Lofthouse
created for each event’s term, or activates it with the event priority if it already
exists. Now revision of knowledge, of the contained beliefs, takes place. It also
holds the implications which were formed by the sensorimotor component, which
manifest as implication links between concepts. The activation of concepts al-
lows the reasoner’s inference to be contextual: only beliefs of the highest priority
concepts, which share a common term with the event selected from the Cycling
Events queue (for Semantic Inference), or are temporally related (through an
implication link or in temporal proximity, for Sensorimotor Inference), will be
retrieved for inference.
4 Operating cycle
The operating cycle of the reasoner makes use of the following attentional control
functions for resource management, these are crucial to make sure the reasoner
works on contextually relevant information.
–Forget event: Forget an event using monotonic decay. This happens in the
cycling events queue, where the decay after selection can differ from the
decay applied over time, dependent on the corresponding event durability
system parameters. (multiplied with the priority to obtain the new one)
–Forget concept: Decay the priority of a concept monotonically over time, by
multiplying with a global concept durability parameter.
–Activate concept: Activate a concept when an event is matched to it in
Concept Memory, proportional to the priority of the event (currently simply
setting concept priority to the matched event’s when its priority exceeds
the concept’s). The idea here is that events can activate concepts while the
concept’s priority leaks over time, so that active concepts tend to be currently
contextually relevant ones (temporally and semantically). Additionally, the
usage counter of the concept gets increased, and the last used parameter set
to the current time, which increases the usefulness of the concept.
–Derive event: The inference results produced (either in Semantic Inference
or Sensorimotor Inference), will be assigned a priority, the product of: belief
concept priority or truth expectation in case of an implication link (context),
Truth expectation of the conclusion (summarized evidence), Priority of the
event which triggered the inference, and 1
log2(1+c)where cis the syntactic
Complexity of the result. (the amount of nodes of the binary tree which
represents the conclusion term)
The multiplication with the parent event priority causes the child event
to have a lower priority than its parent. Now from the the fact that event
durability is smaller than 1, it follows that the cycling events queue elements
will converge to 0 in priority over time when no new input is given. This,
together with the same kind of decay for concept priority, guarantees that
the system will always recover from its attentional states and be ready to
work on new input effectively after busy times.
–Input event: The priority of input events is simply set to 1, it will decay via
relative forgetting as described.
‘OpenNARS for Applications’: Architecture and Control 7
The following overview describes each component of the main operating cycle,
in which the attentional control functions are utilized:
1. Retrieve EVENT SELECTIONS events from cycling events priority queue
(which includes both input and derivations)
2. Process incoming belief events from FIFO, building implications utilizing
input sequences and selected events (from step 1)
3. Process incoming goal events from FIFO, propagating subgoals according to
implications, triggering decisions when above decision threshold
4. Perform inference between selected events and semantically/temporally re-
lated, high-priority concepts to derive and process new events
5. Apply relative forgetting for concepts according to CONCEPT DURABILITY
and events according to EVENT DURABILITY
6. Push selected events (from step 1) back to the queue as well, applying relative
forgetting based on EVENT DURABILITY ON USAGE
Semantic Inference: After an event has been taken out of cycling events
queue, high-priority concepts which either share a common subterm or hold
a temporal link from the selected event’s concept to itself will be chosen for
inference. This is controlled by adapting a dynamic threshold which tries to keep
the amount of selected belief concepts as close as possible to a system parameter.
The selected event will then be taken as the first premise, and the concept’s belief
as the second premise. Here the concept’s predicted or event belief is used when
it’s within a specified temporal window relative to the selected event, otherwise
its eternal belief. The NAL inference rules then derive new events to be added to
cycling events queue, which will then be passed on to concept memory to form
new concepts and beliefs within concepts of same term.
Implication Link formation (Sensorimotor inference): Sequences sug-
gested by the FIFO form concepts and implications. For instance event afollowed
by event b, will create a sequence (a, b), but the sensorimotor inference block will
also make sure that an implication like a⇒bwill be created which will go into
memory to form a link between the corresponding concepts, where aitself can be
a sequence coming from the FIFO sequencer, or a derived event from the cycling
events queue which can help to predict bin the future. Also if a⇒bexists as link
and awas observed, assumption of failure will be applied to the link for implicit
anticipation: if the anticipation fails, the truth expectation of the link will be
reduced by the addition of negative evidence (via an implicit negative bevent),
while the truth expectation will increase due to the positive evidence in case of
success. To solve the Temporal Credit Assignment problem such that delayed
rewards can be dealt with, Eligibility Traces have been introduced in Reinforce-
ment Learning (see [14] and [15]). The idea is to mark the parameters associated
with the event and action which was taken as eligible for being changed, where
the eligibility can accumulate and the eligibility decays over time. Only eligable
state-action pairs will undergo high changes in utility dependent on the received
reward. NARS realizes the same idea via projection and revision: when a con-
clusion is derived from two events, the first event will be penalized in truth value
8 P. Hammer, T. Lofthouse
dependent on the temporal distance to the second event, with a monotonic de-
cay function. If both events have the same term, they will revise with each other
forming a stronger event of same content, capturing the accumulation aspect of
the eligibility trace. If they are different, the implication a⇒bcan be derived
as mentioned before, and if this implication already exists, it will now revise
with the old one, adding the new evidence to the existing evidence to form a
conclusion of higher confidence. If bis a negative event, the truth expectation
will decrease (higher confidence but less frequency), while a positive observation
bwill increase it. This is similar to the utility update in RL, except with one
major difference: the learning rate is not given by the designer, but determined
by the amount of evidence captured so far. In RL implementations this deficit
is compensated by decreasing the learning rate over time with the right speed
(by trial and error carried out by the designer). However given amount of addi-
tional time is not a guarantee that more evidence will be collected for a specific
state-action entry, its state might simply not have re-appeared within the time
window, yet the next time it’s encountered the learning rate for its adjustment
will be lower, leading to inexact credit assignment.
Subgoaling, Prediction and Decision (Sensorimotor inference): When
a goal event enters memory, it triggers a form of sensorimotor inference: sub-
goaling and decision. The method to decide between these two is: the event
concept precondition implication links are checked. If the link is strong enough,
and there is a recent event in the precondition concept (Event aof its concept
when (a, op)⇒gis the implication), it will generate a high desire value for the
reasoner to execute op. The truth expectations of the incoming link desire values
are compared, and the operation from the link with the highest truth expectation
will be executed if over a decision threshold. If not, all the preconditions (such
as a) of the incoming links will be derived as subgoals, competing for attention
and processing in the cycling events queue. Also, event aleads to the prediction
of bvia Deduction, assuming a⇒bexists as implication in concept b.
Motor Babbling: To trigger executions when no procedure knowledge yet
exists, the reasoner periodically invokes random motor operations, a process
called Motor Babbling. Without these initial operations, the reasoner would be
unable to form correlations between action and consequence, effectively making
procedure learning from experience impossible [11], [7] and [6]. Once a certain
level of capability has been reached (sufficient confidence of a procedural impli-
cation (a, op)⇒g), the motor babbling is disabled for op in context a.
5 Experiments & Comparisons
To demonstrate the reasoner’s general purpose capabilities we tested with a
variety of diverse examples using the same default system configuration. The
following examples are all available at the project web site, see [20].
Real-time Q/A. In this example the reasoner needs to answer questions
about drawn shapes in real time (see Fig. 3). Input events consist of shape
instances, their types, and filled property as output by a Convolutional Neural
‘OpenNARS for Applications’: Architecture and Control 9
Network. The shape’s relative location is fed into the reasoner. Queries can be
arbitrary queries such as “What is left of the unfilled circle?”. In our experiment,
the reasoner answered these questions correctly 80 percent of the time within 50
inference steps from 20 example inputs in 10 trials. This were 200 Narsese input
events and 9 seconds per trial, fast enough for real time perception purposes.
Procedure Learning. In the toothbrush example knowledge about different
objects, their properties and what they can be used for is provided (see Fig. 3).
The goal is to unscrew a screw with a toothbrush by melting and reshaping it
into a form usable to unscrew the screw. ONA finds the solution consistently,
within 30 inference steps, while OpenNARS often needs 100K or more.
Generalisation. The goal of this experiment was to show that the reasoner
could learn and then apply generalised procedural knowledge to examples not
previously experienced. The test setup composed of: three switches, with differ-
ent instance names and two operators, ‘goto’ and ‘activate’. From 2 observations
of the user activating switches, the reasoner should learn that the ‘goto’ opera-
tion applied from the start position, will lead to the agent reaching the switch
position. It also learns that when the switch position was reached, and the ‘acti-
vate’ operation is called, the switch will be on. The third switch is then activated
by the reasoner on its own as a solution to the user goal, by invoking ‘goto’ and
‘activate’ on the new switch instance, applying generalised behavior which the
reasoner has learnt to be successful for the previously encountered instances.
Real-time Reasoning. As presented in [5], OpenNARS, was successfully
used to autonomously label regions and to identify jaywalking pedestrians based
on a very minimal background ontology, without scene-specific information,
across a large variety of Streetcams, using a Multi Class Multi Object tracker.
A similar example (capturing key reasoning aspects) is included in the release
of ONA, the new reasoner will replace OpenNARS in future deployments.
Fig. 2: Using minimal scene-independent background knowledge to detect jay-
walking (left), learning to reach and activate switches from observations. (right)
Procedure Execution. Previously, a 24hr reliability test of OpenNARS
v3.0.2 was carried out with the Pong test case. The system ran reliably for the
24hr period with a hit/miss ratio of 2.5 with a learning time of two minutes and
some minor fluctuation in capability in the first 3 hrs. In comparison, OpenNARS
10 P. Hammer, T. Lofthouse
for Applications v0.8.1 ran reliably for the 24hr period with a hit/miss ratio of
156.6 with a learning time of <10 secs and no negative fluctuation. The test for
ONA was more difficult with 3 operations (compared to left/right operations
only for OpenNARS Pong, it didn’t include stop) and approximately 2x faster
ball speed, demanding quicker reaction times.
Fig. 3: Q&A about detected shapes (left), Toothbrush problem solving (right)
6 Conclusion
The decision to take a pragmatic approach to the architecture has proven to
be a worthwhile investment. The change to an event driven control model has
removed much of the complexity of the prior control system. The separation
of semantic and sensorimotor inference has highlighted the key issues of both
aspects whilst avoiding the complexity of a unified handling. The reduction in
complexity has led to many benefits including: simplified parameter tuning, sep-
aration of concerns, and clear attentional focus boundaries.
The use of the meta rule DSL [6] to represent the logic rules allows the rea-
soner to be configured for specific domains. Enabling subsets of inference rules
for specific use cases avoids the processing of unnecessary inference rules and
the resulting increase in non-relevant results. From a software engineering per-
spective, the OpenNARS codebase was well overdue a rewrite as the continuous
incremental change had led to it being difficult to maintain and modify. The
choice of C, utilizing the POSIX API, means the reasoner can be compiled on a
broad range of platforms including embedded, mobile and all major OSs.
In summary, the new architecture and control has led to significant improve-
ments in both efficiency and quality of results, especially in respect to procedure
learning and attention allocation. Connecting to the reasoner via the shell or
UDP protocol is straightforward and tuning the parameters and inference rules
for specific use cases is now possible with minimal effort. The project is open
source, under the MIT license, and available in [20].
‘OpenNARS for Applications’: Architecture and Control 11
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