This paper develops a logical model based on the situation-calculus of the role of indexicality in creating the linguistic context and how the context changes through the actions of the agent. It looks at indexicals of person, place, and time by showing how the egocentric position is linked towards diferent objective "maps' of space and time. Multi-participant discourse sets up relations between between the turn units of conversation, while narrative discourse demands relations between the context and embedded context.
This paper proposes an approach to representing the context created by and used for
interpretation of indexical signs in language (including deictics, conversational sequences, and more as
well) and human behavior (including actions, appearance, etc.). It is based on the integration of
approaches to formalizing context as first-class objects [
The indexical mode of signification [21] can be summarized in the following way:
indexical sign-vehicles point from an origin that is established in, by and ‘at’ their
occuring as the here-and-now ‘center’ or tail, as it were, of a semiotic arrow. At the
terminus of the radial path, or arrowpoint, is their indexical object, no matter what
the perceptual and conceptual dimensions or properties of things indexed [
The work presented here considers only the target representation of the discourse in the framework developed here. The automatic conversion of a textual representation into that used here is not considered at this time. Additionally, methods for reasoning with the represention (i.e., deriving what holds in new contexts) as actions (in particular acts of speaking occur) is not considered. But the reason for utilizing a representation language based on the situation calculus is to make use of the relative large body of literature on automatically deriving conclusions from a set of expressions in the situation calculus.
The representation language based on the situation calculus is described in Section 2. Section 3 discusses the analysis of deictic expressions in natural language. The default egocentric use of these expressions is illustrated in Section 4. An example of narrative discourse is given in Section 5 and an example of conversational discourse is given in Section 6. Finally, in Section 7 the work is briefly summarized and future work is discussed.
Following McCarthy and Buvac˘[
The situation calculus (following the presentation in [22]) is a first-order language for
representing dynamically changing worlds in which all of the changes are the result of named
actions performed by some agent. Here, we merge contexts and states. There is no diference.
If is an action and a situation or context, the result of performing in is represented by
do(, ). The constant c0 is used to denote the initial situation or context. Relations whose
truth values vary from situation to situation are called fluents . Here, following the work on
context, they are reified and represented as terms. Although the use of reified fluents in the
situation calculus is less common (than the alternative approach of using predicate symbols
with a situation argument), it has been used and has been shown to be more expressive [23]. So
here the practice in the literature on contexts is followed. For example, IST(, Broken (obj1))
means that object obj1 is broken in situation . Use of the situation calculus allows one to
represent the efect of the diferent actions on the relevant fluents[
It is necessary to provide for all actions, action pre-condtion axioms, positive-efect axioms, and negative-efect axioms. These axioms are compiled into successor-state axioms that specify completely the truth of fluents in a situation/context in terms of the the truth of those fluents in the preceding situation and the action that was performed to get to the current situation/context. Where convenient, an abbreviation for a sequence of actions is used. For example, instead of do(3, do(2, do(1, ))), an alternative is DO([1, 2, 3], ).
The special predicate ContextCreation(, 1, 2) captures the world creation notion of text
world theory[
The special predicate Refers(, ) is used to indicate that the stretch of speech refers to
object . This is an initial approximation of reference having occurred and a more fine grained
analysis is planned for the future given the complexity of the notion [
Speaking can be represented as with any other action. Certainly in general acts of speaking occur with other actions. We represent acts of speaking as do((, , , )). Here the is the speaker of the utterance, is the transcription of the utterance, and props constitute salient properties of the utterance. These ideally would be automatically extracted from the text of this utterance and others, but for the time being are manually placed in the list props.
Deictics are in the terminology of Jakobson[
Jakobson distinguishes between the narrated event (symbolized as ), the speech event , a participant of the narrated event , and a participant of the speech event . In the representation developed here, is the context created by the action of speaking, while is the context (text world) created by the speech. It is in this context that the actions being talked about actually occur. The participants of the speech event are people who exist in the context in which speaking takes place, while the participants of the narrated event are people who exist in the narrated context, created as a new context within the context in which speech takes place.
Person deixis / relates the participants of the narrated event to those of the speech event. The use of the first-person ( I in English) signals that the participant in the narrated event is identical to the speaker of the speech event. Therefore the first argument to the action speak is identical to the person denoted by I in the context related by the world creation predicate. The second-person (you in English) signals the identity of a participant in the speech event with the hearer in the speaking context.
Tense, symbolized as / relates the time of occurrence of the narrated event to that of
the speech event. The present tense may indicate that the speaking occurs at the same time,
while the future tense may indicate that the narrated event occurs later than the speech event.
The use of tense (along with aspect) in English and in the languages of the world is complex
[
Mood, symbolized as / “characterizes the relation between the narrated event and
its participants with reference to the participants of the speech event[
There is also place deixis [26, 27, 28] that situates an entity in the event of narration spatially with respect to the event of speaking. Examples from English are here, or there. Background knowledge is needed to calibrate the nature of the space. For example, there can refer to the table in view or to some place thousands of miles away. Through the interpretation of deictic expressions, the context is constructed. Examples are found in the following sections.
Deictics combine both a referential and an indexical function [
If the utterance below is said by a detective investigating a crime scene, the interpretation of here is in the very place where the speaker is, or alternatively if the speaker is pointing or glancing towards a place nearby.
do(speak(, 1, [, ℎ15]), )) 1 = ℎ ℎ In props represents the characterization of the utterance as a statement and ℎ15 is a segmented piece of the utterance (the 5th word). We have:
IST(, Arrow(ℎ15, , )) IST(, Refers(ℎ15, )) IST(, Proximal(, )) where = do(speak(, 1, [, ℎ15]))) The in Arrow(ℎ15, , ) stands for egocentric, a default pointing to the current location of the speaker.
In response to a question about where someone’s cofee cup is located, in the following there refers to a place some distance from the speaker, perhaps being “pointed to ” either literally through a pointing action or through a glance.
do(speak(, 2, [, ℎ25], ))
2 = ℎ ℎ In props represents the characterization of the utterance as an answer to a question and ℎ25 is a segmented piece of the utterance (the 5th word). Now, we have:
IST(, Arrow(ℎ25, , )) IST(, Refers(ℎ25, )) IST(, Distal(, )) where = do(speak(, 2, [, ℎ25], ))
Let s1 represent the first sentence from the above account, s2 the second sentence, and s3 the third sentence.
The term c0 is used to denote the initial context. This is the context of what Werth
[
A number of things are asserted within context c0. [Not all are given here.]
IST(do(speak(p1, s1, [, ℎ17, 1,10, 1,4]), c0),
Arrow(ℎ17, , ) ∧ Distal(, ) ∧ Refers(ℎ17, )∧
Refers(1,0, obj2) ∧ Location(obj2, )∧
Refers(1,4, obj1) ∧ Location(obj1, ) ∧ On(obj1, obj2)).
The speaking of the sentence has created what Werth [
ContextCreation(“”, do(speak(p1, s1, ), c0), c1) indicating that there is a new context created in do(speak(p1, s1), c0) through the process of narration and that context is denoted by c1. Additionally, because past tense was used, we indicate that time(c1) < time(do(speak(p1, s1), c0). Since, the act of reading occurred within this text world, there is a new context do(read(p1, obj1), c1).
Within the text world describing the act of saying another text world is established. This is the text world where the police announced the crime and the arrest. We have
ContextCreation(“”, do(read(p1, obj1), c1), c2) indicating that there is a new context created in do(read(p1, obj1), c1) and that context is denoted by c2. Additionally, because past tense was used, the relation time(c2) < time(c1) is added. It is necessary to specify in c2:
Consider the example [30, 31] of a recorded, transcribed, and analyzed conversation between two students at the University of Chicago. It was recorded in a laboratory [32] but seems to be very natural. As is usually the case, there is considerable overlap in the speaking turns of the two participants called Student A and Student B. The situation calculus can represent overlapping actions, but for simplicity this is not represented here.
In the literature on conversation analysis [
Prior to the conversation given here there was a mention of speaker B having been in Iowa before. Hence, we have the indexical invocation of a frame[34, 24] in particular a map of the US and the location of cities and universities. Hence the interpretation of place deictics is with regard to this map as opposed to the default egocentric view. This map is part of the commonsense knowledge of all people connected with universities in some way. With regard to the situation calculus implementation, it is assumed that the map has been specified using sentences of logic. Since the map does not change, the symbols specifying the map are not fluents.
DO([ (, 1, []) (, 13, []) (, 14, []) ], ) 1 = ?´ℎ ′ ℎ
ℎ [to ∅ ] (, 2, [ℎ21]) 2 = ℎ (, 3, [, ℎ36]) 3 = ℎ ℎ ℎ, [] (, 4, [, ℎ46]) 4 = [] ℎ ℎ (, 5, [, ℎ55]) 5 = ℎ ℎ´ ´ [´] (, 6, ) 6 = [´ℎ], ℎ´ℎ (, 7, ) 7 = (, 8, ) 8 = (, 9, ) 9 = [´ℎ], ℎ´ℎ (, 10, [, ℎ10,6]) 10 = ′ ´ ∅, ℎ´ ´ (, 11, []) 11 = ∅ ℎ ´, ℎℎ (, 12, []) 12 = ´ℎ ´ℎ ′ , [ ] 13 = ℎ ℎ′ 14 = , ℎ
Many details of the specification of this example can not be included. Note that in terms of conversational actions, the first question posed by Student A takes place over three utterances and one of those is a contribution of Speaker B. Hence, something like Arrow(1 + 2 + 3, sit, ) is needed to represent that these three utterances together indexically point to the current situation, setting up the expectation that this question will be followed by an answer. The axiomatization needs to ensure that the Arrow relation persists until there is a matching indexical pointing of an answer. This comes with Arrow(4 + 5 + 7, sit, ). Since these two match, the two Arrow relations do not need to persist into future situations. The expectation of an answer has been met.
Again with utterance 10 and 11 we have the same relationship in that Arrow(10, sit, ) sets up the expectation that this question will be followed by an answer. Utterance 11 gives the answer and establishes the relation Arrow(11, sit, ). At this point the expecctation is met and the axiomatization needs to ensure that the two Arrow relations are matched and therefore do not persist. And then again (B begins to ask questions) we have Arrow(13, sit, ) setting up an expectation that is matched by Arrow(14, sit, )
The relationship between conversational actions form a framework within which the deictics of space (and also time) are interpreted. Note that here the referents of the deictics here and there are not the immediate location but rather the location expressed on a map of the US with cities and universities (due to the initial invocation of the frame) in these locations1. The subscript is used for the map.
We see that (in athe appropriate situation)
Arrow(ℎ21, , ) ∧ Refers(ℎ21, ) ∧ Distal(, ) all hold. Note that the indexical pointing to the speaker’s current location is mediated by the map and therefore the deictic refers to an element of the map. The meaning of ℎ46 is handled similarly. But note that in the situation resulting from 5 we have
Arrow(ℎ55, , ) ∧ Refers(ℎ55, ℎ) ∧ Proximal(, ℎ) Later in utterance 10 there is some ambiguity as to whether ℎ10,6 denotes the map of universities or cities. This ambiguity is cleared up in utterance 11, but continues into utterance 14 and utterance 15. This sort of ambiguity among related frames is subtle and is not yet incorporated into this framework.
This paper has proposed a preliminary combination of the situation calculus (used for representing and reasoning about actions in AI) and notions of linguistic context and indexicality from the linguistic, philosophical, sociological, and anthropological literature. Several diferent modes of indexicality have been covered: the egocentric indexicality needed in ordinary deictic reference, reference into embedded worlds, the conversational action that sets up an expectation that it will be followed by an action of the appropriate pair-part and the indexicality needed so that deictic reference is transposed onto a frame (e.g., a map of cities and universities).
For the future, the adaptation of reasoning methods from the situation calculus to this context as well is important. Additionally, (although dificult) the hope is to develop methods to automatically translate written texts into the situation calculus representation. 1This phenomena of the wide range of possibilities for naming locations has been noted by Scheglof [35]. LNAI 9405, Springer, Heidelberg, 2015, pp. 520–425. [21] C. Peirce, Philosophical Writings of Peirce, Dover Publications, New York, 1955. [22] R. Reiter, The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression, in: V. Lifschitz (Ed.), Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, Academic Press, San Diego, CA, 1991, pp. 359–380. [23] J. Pinto, Temporal Reasoning in the Situation Calculus, Ph.D. thesis, Department of Computer Science, University of Toronto, Toronto, Canada, 1994. [24] C. Emmott, Narrative Comprehension: A Discourse Perspective, Clarendon Press, Oxford, 1997. [25] A. Agha, Language and Social Relations, Cambridge University Press, Cambridge, 2007. [26] S. C. Levinson, Pragmatics, Cambridge University Press, Cambridge, England, 1983. [27] C. Fillmore, Lectures on Deixis, CSLI Publications, Stanford, California, 1999. [28] S. Levinson, Deixis, in: L. Horn, G. Ward (Eds.), The Handbook of Pragmatics, Blackwell,
Malden, MA, 2004, pp. 97–121. [29] K. Bühler, The deictic field of language and deictic words, in: R. Jarvella, W. Klein (Eds.), Speech, Place, and Action: Studies in Deixis and Related Topics, John Wiley and Sons, Chichester, 1982, pp. 9–30. [30] M. Silverstein, On the pragmatic ‘poetry’ of prose: Parallelism, repetition, and cohesive structure in the time course of dyadic conversation, in: D. Schifrin (Ed.), Meaning, Form, and Use in Context: Linguistic Applications, Georgetown University Press, Washington, D.C., 1984. [31] M. Silverstein, The improvisational performance of culture in realtime discursive practice, in: R. K. Sawyer (Ed.), Creativity in Performance, Ablex Publishing, Greenwich, Connecticut, 1997, pp. 265–312. [32] S. Duncan, D. Fiske (Eds.), Face-To-Face Interaction, Lawrence Earlbaum Associates, Hillsdale, NJ, 1977. [33] R. B. Scherl, A situation-calculus based model of conversational actions, in: Proceedings, KR4HI 2022: 1st International Workshp on Knowledge Representation for Hybrid Intelligence, Amsterdam, NL, 2022. [34] C. Emmott, Frames of reference: contextual monitoring and the interpretation of narrative discourse, in: M. Coulthard (Ed.), Advances in Written Text Analysis, Routledge, 2000. [35] E. Scheglof, Notes on a conversational practice: Formulating place, in: Studies in Social
Interaction, Free Press, New York, 1972, pp. 75–119. [36] A. Duranti, C. Goodwin (Eds.), Rethinking Context: Language as an interactive phenomenon, Cambridge University Press, Cambridge, England, 1992. [37] A. Duranti, Linguistic Anthropology, Cambridge University Press, Cambridge, 1997. [38] R. I. Binnick, Time and the Verb: A Guide to Tense & Abstract, Oxford University Press,
New York, 1991. [39] B. Comrie, Tense, Cambridge University Press, Cambridge, England, 1985.