Analogical reasoning can be used for plausible inferences based upon direct similarities or structural mappings involving properties and relationships. This can be implemented on top of a combination of symbolic knowledge plus sub-symbolic qualitative metadata, with matching based upon structural or causal similarities, and noticing interesting diferences, in essence, abstracting from similarities and dissimilarities, and will be applied to examples of the form “A is to B as C is to ?X”. A further challenge is to support the use of literal and figurative analogies in natural language, e.g., comparing life to the wheel of fortune, when you want to highlight the role of chance. An easy-to-use syntax will be presented for expressing knowledge, along with a web-based proof of concept demonstrator, and a unifying cognitive architecture for human-like AI. This builds upon pioneering work by Alan Colins on plausible reasoning, and Dedre Gentner on analogies.
The paper starts with an introduction to plausible reasoning before moving on to analogical reasoning and how this can be supported as an extension of plausible reasoning. This very much work in progress, and part of a long term drive to realise human-like memory, reasoning and learning in cognitive agents.
We are learning all the time, and revising our beliefs and understanding as we interact with
others. As such our knowledge is imperfect and subject to uncertainties, incompleteness and
inconsistencies. This is challenging both for conventional mathematical logic, and for statistical
approaches such as Bayesian inference due to the dificulties in obtaining the required statistics.
Evolution has equipped humans with the means to deal with imperfect knowledge in a rational
way based upon sound judgement, albeit subject to various kinds of cognitive biases, see, e.g.,
Daniel Kahneman [
People have studied the principles for plausible arguments since the days of Ancient Greece, e.g., Carneades and his guidelines for argumentation. This was developed further by a long line of philosophers, including Locke, Bentham, Wigmore, Keynes, Wittgenstein, Pollock and many others. Plausible reasoning is everyday reasoning, and the basis for legal, ethical and business discussions. It is now timely to exploit plausible reasoning with imperfect knowledge in support of human-machine cooperative work. This will enable computers to analyse, explain, justify, expand-upon and argue in human-like ways.
Consider → , which means if is true then is true. If is false then may be true or false. If is true, we still can’t be sure that is true, but if is false then must be false. We can go further with a little knowledge. Consider a more concrete example: if it is raining then it is cloudy. This can be used for inferences in both directions. Rain is more likely if it is cloudy, and likewise, if it is not raining, then it might be sunny, so it is less likely that it is cloudy. Such arguments draw upon qualitative terms in lieu of quantitative statistics.
In essence, plausible reasoning draws upon prior knowledge as well as on the role of analogies, and the consideration of examples as precedents. Mathematical proof is replaced by reasonable arguments, both for and against a premise, along with how these are assessed. In legal proceedings, for instance, arguments are laid out by the Prosecution and the Defence, the Judge decides what evidence is admissible, whilst guilt is assessed by the Jury.
During the 1980’s Alan Collins and his co-workers developed a theory of plausible
reasoning [
Plausible knowledge can be expressed using a combination of symbolic graphs and associated
metadata. This paper introduces the plausible knowledge notation (PKN) as an easy-to-read
extensible syntax accompanied with an implementation as a JavaScript library for use in web
page demos for diferent kinds of plausible reasoning [
Relationships f l o w e r s o f E n g l a n d i n c l u d e s d a f f o d i l s , r o s e s ( c e r t a i n t y h i g h ) where flowers is a property of the referent England, and the use of includes signifies that the property is an open set with values daffodils and roses. For a closed set, use is instead of includes. Trailing round brackets are used to list qualitative metadata, in this case declaring that the statement has a high certainty. r o b i n k i n d − o f s o n g b i r d duck s i m i l a r − t o g o o s e f o r h a b i t a t duck d i s s i m i l a r − t o g o o s e f o r neck − l e n g t h where robin is declared as a subclass of songbird, and duck is declared as being similar to goose for habitat and dissimilar to goose in respect to neck length.
c l i m a t e d e p e n d s −on l a t i t u d e p r e s s u r e d e c r e a s e s − w i t h a l t i t u d e c u r r e n t i n c r e a s e s − w i t h v o l t a g e where climate depends on latitude in some unspecified way, whilst pressure decreases with increasing latitude and current increases with increasing voltage.
t e m p e r a t u r e o f ? p l a c e i s warm & r a i n f a l l o f ? p l a c e i s h e a v y i m p l i e s g r a i n o f ? p l a c e i n c l u d e s r i c e Implications are a form of if-then rules where variables are prefixed with a question mark.
Metadata can be given with all kinds of PKN statements. Relationships, dependencies and implications can be used for inferences in both directions, subject to any associated metadata. Following Collins, PKN supports several kinds of statement metadata relevant to diferent kinds of inferences: Typicality in respect to other group members, e.g., robins are typical song birds. Similarity to peers, e.g., having a similar climate.
Strength as conditional likelihood, e.g., the strength of climate for determining which kinds of plants grow well. The forward and backward strengths may difer, e.g., rain is a strong indicator of cloudy weather, whilst cloudy weather is a weak indicator of rain. Frequency as the proportion of children with a given property, e.g., most species of birds have the ability to fly.
Dominance as the relative importance in a given group, e.g., the size of a country’s economy. Multiplicity as the number of items in a given range, e.g., how many diferent kinds of flowers grow in England.
The web demonstrator [
What benefits are potentially possible for analogical reasoning by cognitive agents? A starting point is to distinguish between literal and figurative analogies. The former involves things that are really quite similar, whilst the latter are not obviously comparable at first glance. Analogies can help agents to generalise their knowledge based upon a few examples. This has potential applicability for the properties of things, understanding their behaviours, as well as for problem solving by drawing upon previous experience in similar situations.
Analogies are further related to similes and metaphors in language. Similes involve a
comparison that explicitly emphasises some comparable characteristic, e.g., “his words were like
a punch in the guts” as a way to establish the impact of the words on the listener, whilst
metaphors involve an implicit comparison, e.g., “to get cold feet” is to have second thoughts
about some proposed course of action. People commonly use similes and metaphors to
communicate thoughts in ways that are more vivid and interesting, as well as to structure perceptions
and understanding, see Lackof and Johnson [
Dedre Gentner [
Gentner cites the example of plumbing in that electrical circuits can be likened to a plumbing system for water, e.g., equating voltage to pressure, and electrical current to water flow. Causal relationships for the source can be used to suggest similar relationships for the target, e.g., higher voltage leads to greater current just as higher water pressure leads to greater water flow.
Two situations can be identified as similar if they share some of the same properties, with the implication that you may be able to infer properties of the target from properties of the source. You may also be able to infer relationships, e.g., part/whole or cause/efect. More generally, the situations have diferent properties, that can however be mapped one to another (as in voltage to pressure). Such mappings have to be learned or guessed from matching relationships. Thus, if two situations/contexts have several properties or relationships in common, then we may consider them as analogical equivalents.
The notion of similarity introduced by Collins [
An open question is how people learn such knowledge from examples and being taught by others. That relates to the notion of syntagmatic and paradigmatic learning. Syntagmatic learning deals with learning co-occurrence patterns within episodes, whilst, paradigmatic learning involves identifying generalisations, and is believed to develop at a later age in childhood. Analogies as part of critical thinking. It is easy to find web sites that propose the use of analogies for teaching purposes. These are based upon simple patterns, e.g., synonyms, antonyms, part/whole, cause/efect, etc. Here are some examples: b a t t e r y i s − t o t o r c h a s ? x i s − t o c a r # e n g i n e p o w e r s a c a r i t c h i s − t o s c r a t c h a s ? x i s − t o c o l d # v i r u s c a u s e s a c o l d w a l l i s − t o b r i c k a s b o t t l e i s − t o ? x # a b o t t l e i s made o f g l a s s Solving such queries involves identifying the pattern, and then applying background knowledge. The first step is to recognise the query as using an analogy. The next step is to use the pair that doesn’t involve a variable to identify likely patterns, e.g., battery/torch in the first example. The knowledge base may contain plenty of facts and relationships, and it will be important to look for patterns that also occur for the pair with the variable. It may be the case that two pairs use diferent relationships, in which case, we need to find plausible evidence that they are comparable patterns.
Simple analogies are amenable to a fixed strategy plus associated graph algorithms. Qualitative
metadata can be used to reason about certainty and to prioritise processing. What about more
complicated analogies? The work by Jaime Carbonell on derivational analogies [
The quest for realising human-like AI owes a huge debt to many pioneers over many decades.
To mention just a few: Daniel Kahneman, a Nobel-prize willing psychologist who studied
System 1 & 2 thinking along with cognitive biases [
Figure 1 illustrates a high-level cognitive architecture inspired by the structure and function of the human brain.
Memory is based on graph databases and associated graph algorithms. It combines symbolic graphs with sub-symbolic information, mimicking the human cortex, and defined at a conceptual level above that of RDF and Property Graphs (including NGSI-LD). Recall is stochastic reflecting prior knowledge and past experience. This involves activation boost/decay, spreading activation, the forgetting curve and spacing efect. Perception interprets sensory data at progressively higher levels of abstraction, and places the resulting models into the cortex. Cognitive rules can set the context for perception, and direct attention as needed. Events are signalled by queuing chunks to cognitive bufers to trigger rules describing the appropriate behaviour. A prioritised first-in first-out queue is used to avoid missing closely spaced events.
System 1 is about intuitive/emotional thought, and prioritising what’s important. The limbic system provides rapid automatic assessment of past, present and imagined situations without the delays incurred in deliberative thought. Emotions are perceived as positive or negative, and associated with passive or active responses, involving actual and perceived threats, goal-directed drives and soothing/nurturing behaviours.
System 2 is slower and more deliberate thought, involving sequential execution of rules to carry out particular tasks, including the means to invoke graph algorithms in the cortex, and to invoke operations involving other cognitive circuits. Thought can be expressed at many diferent levels of abstraction, and is subject to control through metacognition, emotional drives, internal and external threats.
Action is about carrying out actions initiated under conscious control, leaving the mind free to work on other things. An example is playing a musical instrument where muscle memory is needed to control your finger placements as thinking explicitly about each finger would be far too slow. The cerebellum provides real-time coordination of muscle activation actively guided by perception.
This architecture has been partially realised with a suite of web-based demos developed for the
W3C Cognitive AI Community Group [
Further work is underway to incrementally realise the requirements identified by Kahneman for System 1, and to understand how plausible reasoning, learning and metacognition can be layered on top of System 1 and 2. This will include the intuitive and deliberative reasoning involved in natural language processing, and the human ability to reason about the past, present, and imagined situations.
AI today can be broadly split into symbolic AI, statistical techniques, and approaches based upon deep learning and multi-layer artificial neural networks. Work in the cognitive sciences suggests a middle ground that combines symbols and sub-symbolic metadata, and is open to distributed representations (e.g., as vectors in noisy high dimensional spaces) where this would yield computational benefits. Traditional symbolic AI is hard to scale, relying on hand-coded knowledge, along with dificulties in dealing with imperfect knowledge, whilst deep learning scales well, but has challenges with reasoning and transparency. This paper draws attention to the potential for mimicking human-like memory, reasoning and learning, inspired by the wealth of research in the cognitive sciences.