The Available definitions of meaning have limitations. A triadic definition is proposed to meet objectives AA and BB.

Meaning is the property of valid expression in Natural Language Text (NLT) along with the context, which is capable of generating “Predefined Responses (PreRes)” from a “Specified Class of Recipients (R)” and the “meaning of NLT for R is PreRes”.

Human Author creates NLT to “describe a concept”.  NLT is “Encoded Concept” and the “meaning of NLT” is “Recreating the Concept form NLT” or “decoding NLT” by “a recipient”.   A well formulated NLT has specific implied questions and answers Q&A-S about the concept according to grammar and dictionary of NL.  Decoding NLT is to derive Q&A corresponding to NLT.  That can be done by a machine as Q&A-M and the recipient as Q&A-R.  If the author has used NL correctly, the Q&A-S and Q&A-M must be the same and machine aided authoring can ensure that.  Recipient (R) for whom NLT is created decodes NLT to find Q&A-R with his or her NL ability.  A machine can compare QA-R and its own Q&A-M to assess the meaning received by R.

The crucial role of recipient in defining meaning is missed earlier.  The new definition enables superior authoring and processing of meaning.  Methods are explained for creating and calibrating "Meaning" and achieving “Semantic interoperability" through machine mediation.

1    Introduction

From a general observation of humans of various ages in different communities it appears that the concept of meaning of actions, gestures, speech, and text is informally and intuitively known to human users.  For most practical purposes, ranging from primitive to philosophical, the humans seem to have grasped the meaning without having to define and agree on the meaning of meaning.  Yet, that is not trivial to ignore nor easy to achieve.  For an information technologist this investigation into the meaning of meaning would have been unnecessary if any of the available definitions were applicable in both human and machine contexts.  This has become necessary because there is a growing need for natural language processing and interfacing and many of the Internet and Web applications seek to be “meaning-centric” with humans and machines participating in creating and acting on the meaning.

Here the focus is on why people communicate in “Natural Language Text (NLT) including context” and what they achieve, so that one can serve the same purpose and achieve the same results when machines are involved.

Accordingly, the objective of this article is AA To define common meaning of Meaning of Natural Language Text (NLT) including context for humans and machines and BB enable both to derive the minimal common meaning for given NLT.  Here the focus is on literal meaning though the approach may be extended to other meanings too.

For this purpose, the representative definitions of meaning form dictionaries and other publications [1 through 9] have been studied for their suitability to satisfy AA and BB above.   From a limited understanding of this study it appears that the available definitions of meaning are not suitable and a comprehensive definition is proposed.

The components of the proposed definition and how they enable authoring and processing of NLT are explained. Although meaning is relative to the recipients, methods are explained for creating and calibrating "Meaning" and achieving “Semantic interoperability" through machine mediation.

2    Available Definitions of Meaning and Limitations

The motivation for looking for the meaning of meaning is explained in the Introduction and the following sources are studied to find suitable definition of meaning.

English Dictionary:

The first (and still the best) and reliable source is found to be English Dictionary.    It gives many meanings, of which “To create significance in the mind” is most relevant though incomplete.  See Section 3.

C K Ogden and I A Richards [1], have made a detailed study of meaning and popularized “meaning triangle”.  It identifies Object (referent), Symbol (word) and explains that Concept is the sense or meaning of the Symbol (word).  They have also described “meaning” as “unprintable mental concept”, which leaves scope for multiple interpretations and uncertainty.  This apart, it is not clear whose mind is involved, writer’s or Reader’s.  This is very crucial and is brought up in Section 3.  Ogden and Richards gave three categories A B and C of meaning, further subdivided into 16 attributes.  But that has not been of much help for AA and BB because they were written in the context of human beings and did not examine the context of machines.  

John F. Sowa [2] described “meaning” and “semantics” and “ontology” extensively in his book. Building on the meaning triangle he presented Frege’s argument that there are more senses beyond reference.  The discussion of “morning star” and “evening star”, both pointing to the same planet Venus, is given as an example of referent being one and senses being two.  In this article, it is pointed out that what are different are the two NLTs “morning star” and “evening star” and the contexts. Here the expressions are different and each expression has corresponding meaning.  It so happens that they lead to the same referent: the planet Venus, which is acceptable.

John Sowa’s [2]  explanation of Charles Sanders Peirce’s three categories, “Firstness, Secondness and Thirdness” and the need for triadic relation M(x,y,z) in defining certain concepts has been most helpful in arriving at the proposed meaning of meaning here.   Although “meaning triangle” identifies three entities it is here pointed out that the entity “Concept” could be in the mind of speaker or reader and could be quite different. This is the lapse that is corrected in the proposed definition.   

Wikipedia

Wikipedia [8,9] is a rich source of information on the meaning of meaning describing the work of Frege, Russell, Boole, Charles Sanders Peirce, Saul Kripke, Alfred North Whitehead, Wittgenstein, Saussure, G. E. Moore, Peter Strawson, Quine, Donald Davidson, Alfred Tarski, Michael Dummett, J. L. Austin, John Searle, Paul Grice, R. M. Hare, R. S. Peters, Jürgen Habermas, Herbert Simon, N. Katherine Hayles.  Books by Paul Horwich 1998, Mark Richard, 2003 [4,5] have also presented analysis and extensions to the theories of meaning by most of those authors.  It has not been possible to specifically recount their theories and assess how far they meet the objectives AA and BB but no direct answers could be found.

Mark Turner [7] has proposed that meaning is necessarily subjective which is valid only in human context.  He argued against the work of Alan Newell and Herbert Simon who built their proposals on the theories of Alfred North Whitehead, Bertrand Russell, Gottlob Frege, the Wittgenstein of the Tractatus, Hobbes, Leibniz, and Descartes. In this article, the subjective nature of meaning is accepted and addressed by including the Recipient R, human or machine, and the Responses of R.  Although humans are capable of defining and understanding higher levels of meaning, it is here proposed that “literal meaning” can be defined and activated in human and machine Recipients interchangeably. That is the common minimal meaning expected in BB.

Artificial Intelligence, Knowledge Representation, Speech and Language Processing

Meaning and understanding are central to these branches of computer science.  They have contributed to representation of knowledge in a machine compatible form for processing, inference, interpretation etc [2,6].  Jurafsky and Martin [6] have presented comprehensive analysis and devoted five chapter to “Representing Meaning”.  They state that “meaning of linguistic utterances can be captured in formal structures”.  It is here pointed out that most natural languages are capable of representing meaning though the expressiveness and precision of the languages may vary.   The need is to define and extract meaning of natural language text—not represent meaning in some formal structures.  If the meaning cannot be represented precisely in a language one may need to improve the grammar and dictionary. That is the motivation for the proposed definition of the meaning in this article.

A worthy reference here is that of Douglas R Hofstadter, “Godel, Echer, Bach: An eternal Golden Braid” [3].   While many of the chapters are relevant to this article, Chapter VI, The Location of Meaning, is directly related.  He examines “whether meaning can be said to be inherent in a message, or whether meaning is always manufactured by the interaction of a mind or a mechanism with a message.  In the latter case, meaning could not said to be located in any single place, or could it be said that a message has any universal, or objective, meaning, since each observer could bring its own meaning to each message.  But in the former case, meaning would have both location and universality.”  The definition proposed in this article answers these questions satisfactorily and leads to the conclusion proposed by him: “That is why the meaning is part of the text itself;”   The next Sentence, “Meaning acts upon intelligence in a predictable way” is a bit confusing. More appropriately, it is argued that what is given is text, not meaning; intelligence (of the recipient R) acts on the text and derives meaning.  So, it becomes necessary to identify a class of R.

3    Defining the Meaning of Meaning—Proposed Definition

The motivation for looking for the meaning of meaning is explained in the previous section.  The dictionary meaning of meaning “To create significance in the mind” is found very suitable though incomplete.  Here, the key and valid entities to be included in triadic definition are identified and elaborated.

The dictionary definition rightly identifies “mind” as a key entity but it leaves out “mind of?”, which is very crucial.  

In the triangle of meaning, Object (referent), Concept (meaning or sense) and Symbol (word) are identified but “Concept in whose mind?” is not stated, which is crucial.  It is here pointed out that one needs to distinguish between Q1 “what is known to the Speaker or Writer or Author?” and Q2 “what is known to the Listener or Reader or Recipient?”

Speaker or Writer or Author knows the Object (which could even be a concept, not a concrete object always) and uses a NLT to identify it or describe it.  The concept in the mind of writer is primary and he creates NLT to represent the concept.  What concept he has in his mind is known only to him and it cannot be accessed.  Only NLT is accessible. Such NLT may be viewed as encoding of concepts that arise in the mind of an author or writer (by imagination or observation).

What is given to the Recipient R is NLT.  He DOES NOT KNOW what the Object is.  He needs to imagine the Object by creating a concept in his mind using NLT.

So, for the definition of “meaning of Natural Language Text NLT” one needs to consider Q2 and the concept created in the mind of Recipient R based on NLT

It is here proposed that “Recipient (R)” must be explicitly included in the definition of meaning.

The next question is, “How does one know What significance is created in the mind of a recipient (R)”? Well, one might say, “ask him or her or it (if it is a machine)”.  This does not solve the problem because one might end up with another “sentence or expression” for which one has to find “the meaning” still, and one would not know how it relates to the first expression.  This would lead to infinite regress drifting away from the purpose of finding “significance” and creating more complications.  This is addressed in the definition here proposed by insisting that to define meaning the response must be elicited from the recipient R.

While the meaning can be applied to a wide range of stimuli, in this article, it is confined to “literal meaning” of valid expression in Natural Language Text (NLT), a phrase and a sentence, extensible to a paragraph.

Based on the above analysis and projection, the following definition is proposed for MEANING.

Meaning is the property of valid expression in Natural Language Text (NLT) along with the context, which is capable of generating “Predefined Responses (PreRes)” from a “Specified Class of Recipients (R)” and the “meaning of NLT for R is PreRes”.

According to this, if a means b, it does not imply that b means a, where a and b are NLT.   If a=b then a and b are equivalent to each other but one is not the meaning of the other.  Actually both produce the same significance in the mind of a recipient but that significance is not the same as NLT whose meaning is sought.

Discussion of the definition:  Is meaning a property?  Yes.  Property of what?  Valid expression in NLT with reference to a specified class of Recipients R.  What is meaning?  Predefined responses (not arbitrary) to the expression.  Who defines it?  A specified class of recipients who use the NLT. The recipients can be a computer program which operates within the syntax and lexicon of the NLT.  The “Predefined Responses” are not exactly “Predefined and stored for all expressions” but they are “predictable (not random or arbitrary) and evoked from defined class of recipients when the expression is presented to them.

4    Explanation of the phrases of the Definition

valid expression (within a language):  The expression itself, a word or  a sentence,  must be consistent with the published / accepted dictionary / glossary of terms,  and grammar (syntax).    Words are short and have well defined meanings in a dictionary and therefore in application.  There are a finite number of words, though large in a rich language.    Phrases are compound words far small in number than number of words.  Sentences are potentially unlimited and their meanings are not predefined in a dictionary but their meanings can be synthesized or composed by following the grammatical rules and meanings of words in a dictionary.

Predefined Responses”:  From the dictionary meaning of meaning, it is recognized that (literal) meaning is the significance generated in the recipient of NLT and so one needs to know what significance is generated in the recipient.  So it is proposed that responses have to be elicited from the recipient with reference to NLT.

Well formed NLT have implied Questions and Answers (defined by grammar and dictionary) and so it is possible to pose those questions and evaluate the answers elicited. This approach can be applied to humans and machines.   There must be one-to-one correspondence between an expression and it’s meaning for the speaker and the listener to reach a common conclusion, that too consistently and repeatedly.

An expression will produce some response, but for any reuse of the expression, the expected response must be predefined.  A word must have the same meaning when ever it is used.  If it assumes different meanings at different times one cannot be sure of what meaning is intended and what meaning is to be inferred.  People normally use only reusable words / expressions and all of them have predefined meanings or they are expected to produce predefined responses.  There could be a defined range of responses.  That range itself can be narrow (fine) or broad (coarse) — both are necessary– depending on the purpose for which the word or a phrase or a sentence is used.

Obtainable from a specified class of recipients:  Although it appears elaborate, one has to acknowledge and accept that there exists a target for communication, explicit or implied.  For certain specialized communications, the recipients must satisfy certain conditions of knowledge to make use of the message in an intended way.  The classes of recipients can be lawyers, scientists of certain disciplines, general public of certain literacy level, etc.  Precision of meaning can be assigned to distinct words by reducing the range of responses to the word from finely classified recipients.   This is often the case with technical or domain specific terms—they have rigidly defined responses but only from a specific group.  So certain trade off is possible.  High precision of a word can be achieved by reducing the expected range of responses or by fine classification of recipients or both.

At this stage it is appropriate to cite the definition given by Bertrand Russell and comment on how it relates to the definition proposed in this paper.  All the notes and observations are given in the table.

Table 1:

Word is a class name of and means “mutually similar occurrences”–Russell

Item / Ref:
Bertrand Russell, An Inquiry into Meaning and Truth.   1938
Intro Page 76
Our Understanding / Comments Relation to our current work and contribution
An Object-word is a class of similar noises or utterances such that from habit, they have become associated with a class of mutually similar occurrences frequently experienced at the same time as one of the noises or utterances in question.  That is to say, let A1, A2, A3 …. Be a set of similar occurrences, and let a1, a2, a3 … be a set of similar noises or utterances; and suppose that when A1 occurred you heard the noise a1, when A2 occurred you heard the noise a2, and so on.  After this has happened a great many times, you notice an occurrence An which is like A1, A2, A3 . . . , and it causes you, by association, to utter or imagine a noise an which is like a1, a2, a3 …If, now, A is a class of mutually similar occurrences of which A1, A2, A3, …An  are members and a  is a class of mutually similar noises or utterances of which a1, a2, a3, . . . .an are members, we may say that a is a word which is the name of the class A, or “means” the class A The focus here is on utterances and variations in them.  So it is elaborate. 
Our input, word, is a string of letters and it is exactly reproduced. So a = a1 = a2 = a3 .. However there could be variations in occurrences A1, A2, A3, …as described.  They correspond to our “range of responses” to input stimulus word a.
Our definition of meaning corresponds exactly to what Russell says.  This is very reassuring. 
This is missing in Miller et al WordNet!

To be developed and converted into a graph, an executable program.  Then there would be an objective definition and activation of “meaning”.

Explicit Meaning –Response:  Given a text NLT, the response is the observable distinct and repeatable reactions (the same text creates the same response) displayed by the recipient entity.  If NLT creates observable reaction in the recipient entity then only it is feasible to assess the responses.  Figure 1 displays the factors and how flow of meaning is made explicit.  But all text input does not necessarily create observable reaction.  Response has to be evoked.

5    Authoring and Interpreting Natural Language Text NLT

Using the proposed definition of “literal meaning”, the processes of authoring NLT and interpreting NLT by independent agents, human or machine, are explained.  Authoring is described as the process of encoding the concept conceived in human mind of the Writer, Author in the form of NLT.  Author needs to know the grammar and vocabulary of the language and use it competently and consistently.  It is argued that Meaning is the recreation of the concept through decoding of NLT by the recipient.  Here the recipient of NLT must also be competent in the natural language but his or her competence may vary causing variation in what he or she could decode or regenerate.

The process of creating NLT is described as “raising and answering a series of questions—Q&A-S” by the Author who is the source of NLT.  A well formulated NLT implies only limited Q and A for each sentence of NLT.  NLT and the corresponding Q&A contain the same information in different forms guided by grammar or syntax of the NLT.  Consider an example  “Tom ate apple”.  Q Who ate? A Tom.  What did Tom eat? A Apple.  What did Tom do? A Eat. What happened to Apple? A It was eaten. Who did what to Apple.  A. Tom, eat.  Here syntax can only provide the structure to post words in the place of Subject, Predicate and Object but cannot ensure that those words are of the right type (parts of speech).  That can also be tested by additional data using a dictionary out of which the words are chosen.  It is the dictionary that forces Predicate to be of the type eat but not drink by examining words in the positions of Subject and Object.  There may be other relevant questions that can be raised by using world knowledge but they do not apply to literal meaning.   The NLT, and hence the implied Q&A-S, would be clear and precise if the grammar and lexicon are well defined and correctly applied.   The purpose of NLT is to convey the meaning to some intended recipients (R).  If the NLT is well formulated, the recipient should be able to give correct answers to the specific questions Q-S implied in the NLT.  All recipients may not be equally competent in the NL and the content or subject but their responses must be within the range implied by the NLT.  The test of grasping the meaning by the recipient is the ability to correctly answer the Q of S. Reciprocally, meaning of NLT is that which is grasped by a class of recipients of given NLT. This is perhaps what Wittgenstein called “meaning is use”.    Different classes of recipients may answer the implied questions differently and to them meanings differ; in the extreme meaning may be lost.  This is the key principle of the proposed definition.  Here the Author or source creates NLT which contains the meaning in the form of implied Q&A-S.  NLT can be delivered to any recipient who may be able to derive Q&A-R.  The extent to which Q&A-R match the Q&A-S define different meanings of NLT relative to different classes of R. See Figure 2.

A significant part of this article is the claim that a computer program can be programmed to analyze NLT and derive implied Q&A-S.  This depends on the explicit rules of grammar and expressive power of the lexicon.

See Figure 1 for the Process Map of how a concept in the mind of author enables him or her to write NLT.  A human editor may help the author to improve his NLT.

6    Encoding Concepts, Deriving Meaning and Evaluation    

Questions to Evoke Response

It is proposed here that a series of questions be derived corresponding to a given NLT and get the recipient R to answer them explicitly. The answers constitute the observable responses.  It is to be noted that all grammatical sentences may not be meaningful i.e., they may not create consistent response.  This may be because of poorly constructed sentences, and poor choice of words or both –i.e.,  There could be lack of meaning at inception.

Here is a summary of what is discussed so far.  What meaning is; what makes it explicit; how to look for and ascertain the meaning etc.  As hinted, creating precise meaning is in proper authoring and tools / aids for the same.  They are described hereafter.

Creation of Text T in Context C
The process of how NLT is created and how Context C is established or implied is not elaborated here because it is an internal process of author’s mind.  Only the human authors are considered here.  Once an author creates Text, which is tangible, one can examine and analyze it.  For that purpose, the author is expected to implicitly or explicitly convey the context in which the NLT is created.

NLT encodes meaning

The syntax of a language is founded on the principle of raising questions and finding answers (Q & A) from within the structure of the sentence.    There are two stages (see Figure 3).  In stage one, the Q and A are based on only the structure of NLT and Context C. This can be considered a schema.  In stage two, the meanings of the words are selected from a dictionary to raise and answer further questions.  This can be considered instances of the schema.  Thus, syntax, combined with an electronic dictionary, gives derived Q&A-M.  This needs to be ratified by subject experts.  Once the automated process matures and human editing becomes unnecessary, the latter may be skipped.  The process yields “Derived Q and A” for NLT.  See Figure 3 Creating NLT and Deriving Q&A (HE & M).

Refinement of NLT or Encoding the Concept.

Syntactic and Semantic Analysis of input NLT leads to generation of Q&A and detection of any ambiguities in NLT.  So, feedback can be provided to the author for clarifications refinement.  If the input NLT is not corrected, the computer program may annotate the NLT with warning/ indication that the input is not clarified or disambiguated.

Deriving Meaning of NLT and Evaluation of Recipients

With reference to Figure 4 there are three factors that determine how a recipient reads and derives meaning of NLT.

1    The NLT itself.  There is not much that can be done at the receiving end.
2    The set of aids used for reading, understanding and arriving at the meaning of the NLT.  Crucial.

2.1    Accumulated knowledge retained in memory -–used mostly is the primary cause of misunderstanding, misinterpretation, confusion, disputes etc. Because of variations in human knowledge and abilities the derived meaning may not match the encoded concept.  This can be corrected and improved.
2.2    Dictionary (semantics)–occasionally used but helpful.
2.3    Books on grammar (syntax)/ punctuation—rarely used, not very critical at the recipient end.  Not using it at the Author end is more critical and detrimental to encoding concept into NLT.  If the reader has doubts then this aid can resolve them if NLT is formulated according to standard syntax and punctuation.

3    The Context.  Usually this is implied or informally conveyed.  It may have to be inferred from the preceding text and text “T” or indirect references / conventions.  

To test and evaluate how meaning is derived, the method proposed here is to pose the Questions derived from NLT to the Recipient R and get him or her to answer the Questions (Respond) based on the NLT received.  The objective comparison and evaluation gives a measurable indication of the meaning transferred. Recipients may have different levels of domain knowledge / language and understand NLT differently.  To neutralize that, the recipients must be qualified and classified.  Otherwise the encoding process may be faulted for no lapse on author’s part or Syntactic and Semantic Analysis.  Well-qualified and intelligent recipients may read more meaning in to the NLT than intended or correct errors / ambiguities of NLT. That also must be avoided to make NLT complete and self-sufficient.  Some of the background applicable must be formally conveyed through Context “C”.  See Figure 1. 

7    Conclusion

The role of recipient in giving meaning to meaning is recognized and a definition is proposed including the recipient and his / her / its responses.  Based on that, good authoring of NLT is identified as a vital factor in generating precise meaning. For that purpose, programmable devices can be of great help since encoding and decoding processes coincide.  Methods are explained for creating and calibrating "Meaning" and achieving “Semantic interoperability" through machine mediation.  Such a combination will achieve a high level of performance, consistency, speed and economy.  In physical tasks and computations this advantage is well realized and exploited.  Now it is the turn of computers in language processing.

Many other research findings which are relevant have not been included to keep within the limits prescribed for the publication.  

8    Acknowledgement

The key concepts of this paper were discussed with the organizers and delegates of Three-Day National Seminar on Language Technology Tools:  Implementation of Telugu.  October 8-10, 2003, University of Hyderabad, Gachibowli.

This is unfunded study / investigation carried out with the cooperation of scholars and professionals at various places.  Professor R M K Sinha and Ms Manju Putcha have provided helpful suggestions to prepare this paper.  Most significant, regular and timely inputs and improvements to the text and graphics of this paper have come from Ms Humera Firdouse, an associate at AMS School of Informatics. 

CMC Limited and AMS School of Informatics provided the environment in which the study / investigations could be carried out. 

9    References: 

[1] Ogden, C K and I A Richards, (1923) The Meaning of Meaning, Hardcourt, Brace and World, New York, 8th ed., 1946.

[2] John F. Sowa, “Knowledge Representation—Logical, Philosophical, and Computational Foundations”,  Copyright © 2000 by Brooks / Cole Thomson Learning ™.
[3] Douglas R Hofstadter, “Godel, Escher, Bach: An eternal Golden Braid",  A metaphorical fugue on minds and machines in the spirit of Lewis Carroll, Copyright © Basic Books Inc., 1979.
[4]  Paul Horwich, Meaning, Published by Oxford University Press, ©1998, ISBN 019823824X, 9780198238249, 241 pages.

[5] Mark Richard, Meaning, Published by Blackwell Publishing, © 2003, ISBN 0631222235, 9780631222231, 341 pages.

[6] Danial Jurafsky and James H. Martin “Speech and Language Processing—An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition”, © 2000 by Pearson Education, Inc. ISBN 81-7808-594-1
[7] Mark Turner,  “Design for a Theory of Meaning”, Copyright © 1992 Published in W. Overton and D. Palermo, editors, The Nature and Ontogenesis of Meaning, Lawrence Erlbaum Associates, 1994, pages 91-107.
[8] Wikipedia http://en.wikipedia.org/wiki/The_Meaning_of_Meaning
[9] http://www.stanford.edu/group/SHR/4-1/text/korb.commentary.html

Figures 1 through Figure 4