Questions, Questions, AAnswers and nswers and PPresuppositions resuppositions

Marie Duží & Martina Číhalová

21.04.2023 Logic Café 3

Queries with Presuppositions Many important features of questions are based on

their presuppositions. Everybody who is at least partially acquainted with the methods applied in social sciences has heard of the importance to consider the presuppositions of a question in questionnaires.

Q: Did you stop smoking?Did you stop smoking? presupposes that you did smoke;

Q: Did all the Did all the trucks deliver their cargo?trucks deliver their cargo?A: Yes.Q: Hence all the cargo has been deliveredHence all the cargo has been delivered? Yes. …

Presupposition: there were some trucks delivering cargo; hence there is some cargo delivered.

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Multi-agent system (MAS)

Taking into account presuppositions of questions is in particular important in case of building a multi-agent system

Autonomous, (less or more) intelligent agents No central dispatcher Agents are active, communicate by messagingcommunicate by messaging,

make decisions, infer consequences, follow their goals

messages: Inform, Order, Query, Unrecognised, … The content of messages is analysed in TIL In order that the system is not prone to

inconsistencies, the agents should communicate in an intelligent way

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Multi-agent system (MAS)

Imagine communication not respecting presuppositions:

Q: Did all the Did all the trucks deliver their cargotrucks deliver their cargo?The system based on FOL:

x Truck(x) Delivered_Cargo(x) Yes (because there are no trucks delivering)

Q: Hence, all the cargo has been deliveredHence, all the cargo has been delivered? Yes (because no cargo has been delivered)

OK, I will inform the sellers that the goods have arrived

???

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QUESTIONS AND ANSWERS

The question posed by an empirical interrogative empirical interrogative sentencesentence S is the -intension denoted by S. Hence, the question is an -intension of type whose

-value in the actual world w and time t the questioner would like to know.

a direct answer to the question Q is a construction of an -value of Q-value of Q in a given world-time pair of evaluation.

a complete answer to the question Q is a construction of the proposition that the -value of Q-value of Q is a is a

The type of a Yes/No question is a proposition; hence, a direct answer provides a truth-value.

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Wh-questions Who is ... ?

Who is the Mayor of Ostrava?wt [0Mayor_ofwt 0Ostrava] Types: Mayor_of/(); Ostrava/.

Which ...? Which mobile agents are going to Prague? wt x [[[0Mobile 0Agent]wt x]

[0Going_towt x 0Prague]] () Types: Mobile/(()()): a property modifier;

Agent/(); Going_to/(); Prague/.

Open issue: do wh-questions come attached with a presupposition?

(In our opinion, yes, but not the above ones.)

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Exclusive-or questions: ..., or... ?

““Is the parking lot Is the parking lot PP11 vacant or vacant or occupied?”occupied?”

The answer will not be Yes/No (not inclusive but exclusive or); rather, the answer conveys one of the properties vacant, occupied

wt [0I p [[pwt 0P1] [[p = 0Vacant] [p = 0Occupied]]]] Types: p/*1 v (); I/(()(())): the ()-

singularizer; P1/; Vacant, Occupied/().

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Presupposition of a question Standard definition: What is presupposed must be true under each

answer to a question. In other words, a presupposition is entailed by each complete presupposition is entailed by each complete answer to the questionanswer to the question. Works well in case of positive answers, but negative

answers are problematic

Complete answer is a propositional construction. “Who is the Mayor of Ostrava?” Direct answer: ‘Mr. Kajnar’. Complete answer:

“The Mayor of Ostrava is Mr. Kajnar”.

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Presupposition vs. mere entailment

(i) P is a presupposition of S:(S |= P) and (non-S |= P)Corollary: If non-P then neither S nor non-S is true; S has no truth-value.

(ii) S merely entails (but does not presuppose) P:(S |= P) and neither (non-S |= P) nor (non-S |= non-P)

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Presupposition vs. mere entailmentWe follow Frege and Strawson in treating survival survival

under negationunder negation as the most important test for presupposition.

But a negative answer to a question is often ambiguous. The ambiguity consists in not distinguishing between two kinds of negative answers, to wit the answers applying anarrow-scope negation narrow-scope negation and wide-scope wide-scope negationnegation.

While the former preserves presupposition, the latter seems to be presupposition denying.

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Two kinds of negation

Q: Did you stop beating your wife?A: NoQ: Hence you still beat her?

It is not true that I stopped …(wide-scope)

A: No (?)I did not stop … (narrow scope)

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Two kinds of negationQ: Who is the Mayor of OstravaWho is the Mayor of Ostrava?

A: Tomáš Machura (or Petr Kajnar, or, …) the Mayor exists

A: Nobody (the office is not occupied, the Mayor does not exist)

mere entailmentmere entailment

Q: When did the (current) Mayor of Ostrava visit PragueWhen did the (current) Mayor of Ostrava visit Prague?

A: Never ???It is not true that the Mayor visited Prague (because the Mayor does not exist)

The Mayor did not visit Prague

presupposition presupposition that the Mayor exists

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Two kinds of negationIn the logic of partial functions such as TIL these two kinds of negation are not equivalentare not equivalent Narrow-scope: „X did not stopdid not stop beating his wife“ Wide-scope: „It is not true thatIt is not true that X stopped beating his wife“

Presuppositions: X has been married; X did beat his wife; …

NsN: the property of having stopped … is negated

WsN: the entire proposition that X stopped … is negated

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Two kinds of negation

Propos. Presupp. NsN WsN

X stopped A X did A X did not stop A It is not true that X stopped A

T T F F

F T T T

F T

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Presupposition of a question

Negative direct answer – only the interpretation applying the narrow scope negation preserving presupposition is adequate Presupposition of an empirical question Q is Presupposition of an empirical question Q is

a proposition Pa proposition P that is entailed by every that is entailed by every complete answer corresponding to the complete answer corresponding to the respective unambiguous direct answerrespective unambiguous direct answer

Instead of a wide-scope negation an adequate complete answercomplete answer is then a negated presupposition I have not been married, I did not beat my wife,

The Mayor of Ostrava does not exist, …

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Answering in TIL

The agent must first check whether the presupposition of a question is true; if it is not so, then the answer is answer is the negated presuppositionthe negated presupposition

If Presuppositionthan direct answer else negated presupposition

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TIL definition of If P then C else D

1. Make a choice between C and D based on P: [0The_only c [[P [c = 0C]] [P [c = 0D]]]]

2. Execute the chosen construction c2[0The_only c [[P [c = 0C]] [P [c = 0D]]]]

The_only is a singulariser function ({n} n) that returns the only construction, the member of a singleton; otherwise undefined

c n: a variable ranging over procedures; 0C, 0D: procedures C, D are objects to operate on; Hyperintensional logic is needed to deal with

procedures, not only with their products.

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Answering in TIL If there are some trucks delivering their

cargo than T or F according as all of them delivered the cargo, else no trucks (negated presupposition)

TIL analysis (schematic):

wwtt IfIf [[ [[00Some Some 00TrucksTruckswtwt] ] 00DeliveringDeliveringwtwt] ]

than than [[[[00All All 00TrucksTruckswtwt] ] 00DeliveredDeliveredwtwt]] else else [[[[00No No 00TrucksTruckswtwt] ] 00DeliveringDeliveringwtwt]]

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Presupposition triggers Topic-focus articulation

Topic presupposition Focus mere entailment

Interruption/termination of an activity Presupposes that the activity took place

Future/past tenses with reference time The time t of evaluation must be less than / greater

than the reference time T Factiva in attitudes

know that, regret that, … Exclusive-or

Just one alternative

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Interruption/termination of an activity Did Tom find a nearby vacant parkingDid Tom find a nearby vacant parking?

Merely entailsMerely entails but does not presupposedoes not presuppose that a nearby vacant parking exists (Karttunen ‘semifactivum’)

PresupposesPresupposes that Tom had been looking for a nearby vacant parking

wt [If t’ [[t’ < t] [0Seekwt‘ 0Tom 0Parking]]

then [0Findwt 0Tom 0Parking]

else t’ [[t’ < t] [0Seekwt‘ 0Tom 0Parking]]

]Types: , /(()); Seek, Find/(()); Parking/().

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Dynamic querying; tenses Another frequent case of queries with

presuppositions are queries in future or past tenses with a reference time informing when this or that should happen or happened, respectively.

Consider, for instance, this situation: a sends to b a query-message

“Shall we meet today at 4 p.m.?” and b obtains the message at 5 p.m. Now b cannot possibly answer Yes or No.

Instead, b should inform a that the time of evaluation of this message is greater than the time specified by the message.

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Queries and tenses

wt [If [t < 04] then

[[[0Meet w] 04] a b] [[0Today t] 04]] else [t 04] ]

Types. 4/t: the time moment 4 p.m. of the respective day; Meet/(); Today/(()).

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ConclusionThe main contribution is the analysis of questionsquestions that

come attached with a presuppositionpresupposition. By distinguishing two kinds of negation, we managed to

make the commonly used definition of presupposition of definition of presupposition of a question more accuratea question more accurate.

Another contribution is the analysis of the appropriate appropriate answering reactionanswering reaction. If the presupposition of a question Q is not true, then there is no direct answer, that is, the agent asked cannot convey the value of Q. Instead, the agent informs the inquirer that the presupposition is not true, which makes it possible to adjust the question.

We also considered several presupposition triggerspresupposition triggers, and using our general analytic schemageneral analytic schema that applies the strict TIL definition of the ‘if-then-else’ function, we analysed answering these types of questions.

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Thank you for your attention

Questions?Answers?

Presuppositions !!!