An operational definition of "meaning" (in a formal language)

Working notion of meaning

... we shall accept that the meaning of A is the set of sentences S true because of A. The set S may also be called the set of consequences of A. Calling sentences of S consequences of A underscores the fact that there is an underlying logic which allows one to deduce that a sentence is a consequence of A.

Wladyslaw M. Turski and Thomas S. E. Maibaum, The specification of computer programs (Wokingham: Addison-Wesley, 1987), p. 4.

cited in: C. M. Sperberg-McQueen, Meaning and interpretation of markup: a report on the Bechamel Project, slides from talk sponsored by the W3C German/Austrian Office at the Fraunhofer Gesellschaft Institut Medienkommunikation in Sankt Augustin, Germany, 1 October 2004.

How would one define "the epistemic sense of the utterance of a natural language expression"? What is the semantic contribution of individual lexical items that occur in that expression?

The slides are about the meaning of markup, which is a technological vocabulary for describing the representamen of a text (a character stream in Unicode, a layer of content and markup, a layer of syntax tree, a layer of Infoset graph). The representamen of a text or expression is described in terms of a type-vocabulary for its parts.

So ...

• what inferences are licensed by each element type?
• by each attribute?
• for each location? (i.e. how do you associate the meaning with a particular instance?)

Part of the use-context of markup is it describes parts of the representamen that currently or at some time may get different treatment, in terms of stylistic rendering or some other (semantic?) application. Element names are typically in the everyday language of users of the text. Attribute names tend to be more technical, of interest more to technologists than end-users.

Some premises

• Rules are vocabulary-specific.
• The coding a is both visually and semantically parallel to Fa
• Definition of F to be provided ...
• In many cases, the relevant property has arity > 1: F(a,b), F(a,b,c), ...
• As a consequence:
• We need deixis.
• Argument structure is crucial.

This may embody a rather extensional view of the representamen. The minimal character strings are individuals, an element type is predicated of one or more individuals. Deixis implies a need for reflexive content as well as referential.

• Challenges:
• technical / plumbing
  • distributed / non-distributed properties
  • overriding inheritance
  • milestone elements
  • unique identity of individuals


• design / philosophical
  
  • completeness
  • Can we really expect to list "all and only the inferences licensed by the markup"?
  • No: we cannot list them all (infinite set).
  • We may be able to identify a basis (a finite set of sentences from which the members of the infinite set follow).
  • Or maybe not?
  • fertile valley vs. desert landscape
  • meta-markup

A ‘desert landscape’ view

The Wittgenstein transcripts postulate

• the manuscript
• the transcription
• pages
• text blocks (main block, left margin, ...)
• characters

And possibly also

• the von Wright catalog and its entries
• words and sentences as described by Duden
• people
• dates
• MECS-WIT version numbers

The name desert landscape is borrowed from W.V.O. Quine.

A ‘fertile valley’ view

We may also postulate

• sections
• revisions
• acts of deletion
• insertions
• formulae
• quotations
• names, dates, things, ...

Markup is not used to classify utterances signaling a speech act display. Historically, it emerged to classify a text as a renderable document. This is a display of a persistent artifact, made of parts which are visually distinguishable in the rendering.