Downward entailment

Main article: Downward entailing

All downward entailing contexts are nonveridical. Because of this, theories based on nonveridicality can be seen as extending those based on downward entailment, allowing more cases of polarity item licensing to be explained.

Downward entailment predicts that polarity items will be licensed in the scope of negation, downward entailing quantifiers like few N, at most n N, no N, and the restriction of every:

No students saw anything.

Mary didn't see anything.

Few children saw anything.

Every student who saw anything should report to the police.

>>15906189

>Main article: Downward entailing

In linguistic semantics, a downward entailing (DE) propositional operator is one that constrains the meaning of an expression to a lower number or degree than would be possible without the expression. For example, "not," "nobody," "few people," "at most two boys." Conversely, an upward-entailing operator constrains the meaning of an expression to a higher number or degree, for example "more than one." A context that is neither downward nor upward entailing is non-monotone[citation needed], such as "exactly five."

A downward-entailing operator reverses the relation of semantic strength among expressions. An expression like "run fast" is semantically stronger than the expression "run" since "John ran fast" entails "John ran," but not conversely. But a downward-entailing context reverses this strength; for example, the proposition "At most two boys ran" entails that "At most two boys ran fast" but not the other way around.

An upward-entailing operator preserves the relation of semantic strength among a set of expressions; for example "more than three ran fast" entails "more than three ran" but not the other way around.

Ladusaw (1980) proposed that downward entailment is the property that licenses polarity items. Indeed, "Nobody saw anything" is downward entailing and admits the negative polarity item anything, while *"I saw anything" is ungrammatical (the upward-entailing context does not license such a polarity item). This approach explains many but not all typical cases of polarity item sensitivity. Subsequent attempts to describe the behavior of polarity items rely on a broader notion of nonveridicality.

>>15906093

people that want their genitals surgically mutilated

obviously need professional

surgical genital mutilation

>>15906190

>entailing

Strawson-DE

Downward entailment does not explain the licensing of any in certain contexts such as with only:

Only John ate any vegetables for breakfast.

This is not a downward-entailing context because the above proposition does not entail “Only John ate kale for breakfast” (John may have eaten spinach, for example).

Von Fintel (1999) claims that although only does not exhibit the classical DE pattern, it can be shown to be DE in a special way. He defines a notion of Strawson-DE for expressions that come with presuppositions. The reasoning scheme is as follows:

P → Q

[[ only John ]] (P) is defined.

[[ only John ]] (Q) is true.

Therefore, [[ only John ]] (P) is true.

Here, (2) is the intended presupposition. For example:

Kale is a vegetable.

Somebody ate kale for breakfast.

Only John ate any vegetables for breakfast.

Therefore, only John ate kale for breakfast.

Hence only is a Strawson-DE and therefore licenses any.

Giannakidou (2002) argues that Strawson-DE allows not just the presupposition of the evaluated sentence but just any arbitrary proposition to count as relevant. This results in over-generalization that validates the use if any in contexts where it is, in fact, ungrammatical, such as clefts, preposed exhaustive focus, and each/both:

* It was John who talked to anybody.

* John talked to anybody.

* Each student who saw anything reported to the Dean.

* Both students who saw anything reported to the Dean.

>>15906200

>>entailing

Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additionalassumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment is monotone if and only if the rule is admissible. Logical systems with this property are occasionally called monotonic logics in order to differentiate them from non-monotonic logics.

>>15906211

>>>entailing

Weakening rule

To illustrate, consider the natural deduction sequent:

Γ ⊢ {\displaystyle \vdash } \vdash C

That is, on the basis of a list ofassumptions Γ, one can prove C. Weakening, by adding anassumption A, allows one to conclude:

Γ, A ⊢ {\displaystyle \vdash } \vdash C

For example, the syllogism "All men are mortal. Socrates is a man. Therefore Socrates is mortal." can be weakened by adding a premise: "All men are mortal. Socrates is a man. Cows produce milk. Therefore Socrates is mortal." The validity of the original conclusion is not changed by the addition of premises.

In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James Park,[1] in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist (the same result would be independently derived in 1982 by Wootters and Zurek[2] as well as Dieks[3] the same year). The aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors. For example, one might use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits without violating the no-cloning theorem as no well-defined state may be defined in terms of a subsystem of an entangled state. The no-cloning theorem (as generally understood) concerns only pure states whereas the generalized statement regarding mixed states is known as the no-broadcast theorem.

The no-cloning theorem has a time-reversed dual, the no-deleting theorem. Together, these underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger compact category.[4][5] This formulation, known as categorical quantum mechanics, allows, in turn, a connection to be made from quantum mechanics to linear logic as the logic of quantum information theory (in the same sense that intuitionistic logic arises from Cartesian closed categories).

>>15906217

>That is, on the basis of a list ofass2assumption A, allows one to conclude:

>>15906222

History

According to Asher Peres[6] and David Kaiser,[7] the publication of the 1982 proof of the no-cloning theorem by Wootters and Zurek[2] and by Dieks[3] was prompted by a proposal of Nick Herbert[8] for a superluminal communication device using quantum entanglement, and Giancarlo Ghirardi[9] had proven the theorem 18 months prior to the published proof by Wootters and Zurek in his referee report to said proposal (as evidenced by a letter from the editor[9]). However, Ortigoso[10] pointed out in 2018 that a complete proof along with an interpretation in terms of the lack of simple nondisturbing measurements in quantum mechanics was already delivered by Park in 1970.[1]

>>15906231

Theorem and proof

Suppose we have two quantum systems A and B with a common Hilbert space H = H A = H B {\displaystyle H=H_{A}=H_{B}} {\displaystyle H=H_{A}=H_{B}}. Suppose we want to have a procedure to copy the state | ϕ ⟩ A {\displaystyle |\phi \rangle {A}} |\phi \rangle {A} of quantum system A, over the state | e ⟩ B {\displaystyle |e\rangle {B}} |e\rangle {B} of quantum system B, for any original state | ϕ ⟩ A {\displaystyle |\phi \rangle {A}} |\phi \rangle {A} (see bra–ket notation). That is, beginning with the state | ϕ ⟩ A ⊗ | e ⟩ B {\displaystyle |\phi \rangle {A}\otimes |e\rangle {B}} {\displaystyle |\phi \rangle {A}\otimes |e\rangle {B}}, we want to end up with the state | ϕ ⟩ A ⊗ | ϕ ⟩ B {\displaystyle |\phi \rangle {A}\otimes |\phi \rangle {B}} {\displaystyle |\phi \rangle {A}\otimes |\phi \rangle {B}}. To make a "copy" of the state A, we combine it with system B in some unknown initial, or blank, state | e ⟩ B {\displaystyle |e\rangle {B}} |e\rangle {B} independent of | ϕ ⟩ A {\displaystyle |\phi \rangle {A}} |\phi \rangle {A}, of which we have no prior knowledge.

The state of the initial composite system is then described by the following tensor product:

| ϕ ⟩ A ⊗ | e ⟩ B . {\displaystyle |\phi \rangle {A}\otimes |e\rangle {B}.} {\displaystyle |\phi \rangle {A}\otimes |e\rangle {B}.}

(in the following we will omit the ⊗ {\displaystyle \otimes } \otimes symbol and keep it implicit).

There are only two permissible quantum operations with which we may manipulate the composite system:

We can perform an observation, which irreversibly collapses the system into some eigenstate of an observable, corrupting the information contained in the qubit(s). This is obviously not what we want.

Alternatively, we could control the Hamiltonian of the combined system, and thus the time-evolution operator U(t), e.g. for a time-independent Hamiltonian, U ( t ) = e − i H t / ℏ {\displaystyle U(t)=e^{-iHt/\hbar }} {\displaystyle U(t)=e^{-iHt/\hbar }}. Evolving up to some fixed time t 0 {\displaystyle t_{0}} t_{0} yields a unitary operator U on H ⊗ H {\displaystyle H\otimes H} H\otimes H, the Hilbert space of the combined system. However, no such unitary operator U can clone all states.

The no-cloning theorem answers the following question in the negative: Is it possible to construct a unitary operator U, acting on H A ⊗ H B = H ⊗ H {\displaystyle H_{A}\otimes H_{B}=H\otimes H} {\displaystyle H_{A}\otimes H_{B}=H\otimes H}, under which the state the system B is in always evolves into the state the system A is in, regardless of the state system A is in?

Theorem: There is no unitary operator U on H ⊗ H {\displaystyle H\otimes H} H\otimes H such that for all normalised states | ϕ ⟩ A {\displaystyle |\phi \rangle {A}} {\displaystyle |\phi \rangle {A}} and | e ⟩ B {\displaystyle |e\rangle {B}} |e\rangle {B} in H {\displaystyle H} H

U ( | ϕ ⟩ A | e ⟩ B ) = e i α ( ϕ , e ) | ϕ ⟩ A | ϕ ⟩ B {\displaystyle U(|\phi \rangle {A}|e\rangle {B})=e^{i\alpha (\phi ,e)}|\phi \rangle {A}|\phi \rangle {B}} {\displaystyle U(|\phi \rangle {A}|e\rangle {B})=e^{i\alpha (\phi ,e)}|\phi \rangle {A}|\phi \rangle {B}}

for some real number α {\displaystyle \alpha } \alpha depending on ϕ {\displaystyle \phi } \phi and e {\displaystyle e} e.

The extra phase factor expresses the fact that a quantum-mechanical state defines a normalised vector in Hilbert space only up to a phase factor i.e. as an element of projectivised Hilbert space.

To prove the theorem, we select an arbitrary pair of states | ϕ ⟩ A {\displaystyle |\phi \rangle {A}} |\phi \rangle {A} and | ψ ⟩ A {\displaystyle |\psi \rangle _{A}} |\psi\rangle_A in the Hilbert space H {\displaystyle H} H. Because U is supposed to be unitary, we would have

⟨ ϕ | ψ ⟩ ⟨ e | e ⟩ ≡ ⟨ ϕ | A ⟨ e | B | ψ ⟩ A | e ⟩ B = ⟨ ϕ | A ⟨ e | B U † U | ψ ⟩ A | e ⟩ B = e − i ( α ( ϕ , e ) − α ( ψ , e ) ) ⟨ ϕ | A ⟨ ϕ | B | ψ ⟩ A | ψ ⟩ B ≡ e − i ( α ( ϕ , e ) − α ( ψ , e ) ) ⟨ ϕ | ψ ⟩ 2 . {\displaystyle \langle \phi |\psi \rangle \langle e|e\rangle \equiv \langle \phi |{A}\langle e|{B}|\psi \rangle {A}|e\rangle {B}=\langle \phi |{A}\langle e|{B}U^{\dagger }U|\psi \rangle {A}|e\rangle {B}=e^{-i(\alpha (\phi ,e)-\alpha (\psi ,e))}\langle \phi |{A}\langle \phi |{B}|\psi \rangle {A}|\psi \rangle {B}\equiv e^{-i(\alpha (\phi ,e)-\alpha (\psi ,e))}\langle \phi |\psi \rangle ^{2}.} {\displaystyle \langle \phi |\psi \rangle \langle e|e\rangle \equiv \langle \phi |{A}\langle e|{B}|\psi \rangle {A}|e\rangle {B}=\langle \phi |{A}\langle e|{B}U^{\dagger }U|\psi \rangle {A}|e\rangle {B}=e^{-i(\alpha (\phi ,e)-\alpha (\psi ,e))}\langle \phi |{A}\langle \phi |{B}|\psi \rangle {A}|\psi \rangle {B}\equiv e^{-i(\alpha (\phi ,e)-\alpha (\psi ,e))}\langle \phi |\psi \rangle ^{2}.}

Since the quantum state | e ⟩ {\displaystyle |e\rangle } |e\rangle is assumed to be normalized, we thus get

>>15906240

| ⟨ ϕ | ψ ⟩ | 2 = | ⟨ ϕ | ψ ⟩ | . {\displaystyle |\langle \phi |\psi \rangle |^{2}=|\langle \phi |\psi \rangle |.} {\displaystyle |\langle \phi |\psi \rangle |^{2}=|\langle \phi |\psi \rangle |.}

This implies that either | ⟨ ϕ | ψ ⟩ | = 1 {\displaystyle |\langle \phi |\psi \rangle |=1} {\displaystyle |\langle \phi |\psi \rangle |=1} or | ⟨ ϕ | ψ ⟩ | = 0 {\displaystyle |\langle \phi |\psi \rangle |=0} {\displaystyle |\langle \phi |\psi \rangle |=0}. Hence by the Cauchy–Schwarz inequality either ϕ = e i β ψ {\displaystyle \phi =e^{i\beta }\psi } {\displaystyle \phi =e^{i\beta }\psi } or ϕ {\displaystyle \phi } \phi is orthogonal to ψ {\displaystyle \psi } \psi . However, this cannot be the case for two arbitrary states. Therefore, a single universal U cannot clone a general quantum state. This proves the no-cloning theorem.

Take a qubit for example. It can be represented by two complex numbers, called probability amplitudes (normalised to 1), that is three real numbers (two polar angles and one radius). Copying three numbers on a classical computer using any copy and paste operation is trivial (up to a finite precision) but the problem manifests if the qubit is unitarily transformed (e.g. by the Hadamard quantum gate) to be polarised (which unitary transformation is a surjective isometry). In such a case the qubit can be represented by just two real numbers (one polar angle and one radius equal to 1), while the value of the third can be arbitrary in such a representation. Yet a realisation of a qubit (polarisation-encoded photon, for example) is capable of storing the whole qubit information support within its "structure". Thus no single universal unitary evolution U can clone an arbitrary quantum state according to the no-cloning theorem. It would have to depend on the transformed qubit (initial) state and thus would not have been universal.

>>15906242

>assical computer using any copy and paste operation is trivial

In the statement of the theorem, two assumptions were made: the state to be copied is a pure state and the proposed copier acts via unitary time evolution. Theseassumptions cause no loss of generality. If the state to be copied is a mixed state, it can be purified.[clarification needed] Alternately, a different proof can be given that works directly with mixed states; in this case, the theorem is often known as the no-broadcast theorem.[11][12] Similarly, an arbitrary quantum operation can be implemented via introducing an ancilla and performing a suitable unitary evolution.[clarification needed] Thus the no-cloning theorem holds in full generality.

Similarly, cloning would violate the no-teleportation theorem, which says that it is impossible to convert a quantum state into a sequence of classical bits (even an infinite sequence of bits), copy those bits to some new location, and recreate a copy of the original quantum state in the new location. This should not be confused with entanglement-assisted teleportation, which does allow a quantum state to be destroyed in one location, and an exact copy to be recreated in another location.

The no-cloning theorem is implied by the no-communication theorem, which states that quantum entanglement cannot be used to transmit classical information (whether superluminally, or slower). That is, cloning, together with entanglement, would allow such communication to occur. To see this, consider the EPR thought experiment, and suppose quantum states could be cloned.Assume parts of a maximally entangled Bell state are distributed to Alice and Bob. Alice could send bits to Bob in the following way: If Alice wishes to transmit a "0", she measures the spin of her electron in the z direction, collapsing Bob's state to either | z + ⟩ B {\displaystyle |z+\rangle {B}} |z+\rangle {B} or | z − ⟩ B {\displaystyle |z-\rangle {B}} |z-\rangle {B}. To transmit "1", Alice does nothing to her qubit. Bob creates many copies of his electron's state, and measures the spin of each copy in the z direction. Bob will know that Alice has transmitted a "0" if all his measurements will produce the same result; otherwise, his measurements will have outcomes | z + ⟩ B {\displaystyle |z+\rangle {B}} |z+\rangle {B} or | z − ⟩ B {\displaystyle |z-\rangle {B}} |z-\rangle {B} with equal probability. This would allow Alice and Bob to communicate classical bits between each other (possibly across space-like separations, violating causality).

Quantum states cannot be discriminated perfectly.[13]

The no cloning theorem prevents an interpretation of the holographic principle for black holes as meaning that there are two copies of information, one lying at the event horizon and the other in the black hole interior. This leads to more radical interpretations, such as black hole complementarity.

The no-cloning theorem applies to all dagger compact categories: there is no universal cloning morphism for any non-trivial category of this kind.[14] Although the theorem is inherent in the definition of this category, it is not trivial to see that this is so; the insight is important, as this category includes things that are not finite-dimensional Hilbert spaces, including the category of sets and relations and the category of cobordisms.

Imperfect cloning

Even though it is impossible to make perfect copies of an unknown quantum state, it is possible to produce imperfect copies. This can be done by coupling a larger auxiliary system to the system that is to be cloned, and applying a unitary transformation to the combined system. If the unitary transformation is chosen correctly, several components of the combined system will evolve into approximate copies of the original system. In 1996, V. Buzek and M. Hillery showed that a universal cloning machine can make a clone of an unknown state with the surprisingly high fidelity of 5/6.[15]

Imperfect quantum cloning can be used as an eavesdropping attack on quantum cryptography protocols, among other uses in quantum information science.

An implicature is something the speaker suggests or implies with an utterance, even though it is not literally expressed. Implicatures can aid in communicating more efficiently than by explicitly saying everything we want to communicate.[1] This phenomenon is part of pragmatics, a subdiscipline of linguistics. The philosopher H. P. Grice coined the term in 1975. Grice distinguished conversational implicatures, which arise because speakers are expected to respect general rules of conversation, and conventional ones, which are tied to certain words such as "but" or "therefore".[2] Take for example the following exchange:

A (to passer by): I am out of gas.

B: There is a gas station 'round the corner.

Here, B does not say, but conversationally implicates, that the gas station is open, because otherwise his utterance would not be relevant in the context.[3][4] Conversational implicatures are classically seen as contrasting with entailments: They are not necessary or logical consequences of what is said, but are defeasible (cancellable).[5][6] So, B could continue without contradiction:

B: But unfortunately it's closed today.

An example of a conventional implicature is "Donovan is poor but happy", where the word "but" implicates a sense of contrast between being poor and being happy.[7]

Later linguists introduced refined and different definitions of the term, leading to somewhat different ideas about which parts of the information conveyed by an utterance are actually implicatures and which are not.[8][9]

Conversational implicature

Grice was primarily concerned with conversational implicatures. Like all implicatures, these are part of what is communicated. In other words, conclusions the addressee draws from an utterance although they were not actively conveyed by the communicator are never implicatures. According to Grice, conversational implicatures arise because communicating people are expected by their addressees to obey the maxims of conversation and the overarching cooperative principle, which basically states that people are expected to communicate in a cooperative, helpful way.[10][11]

The cooperative principle Make your contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged.

The maxims of conversation

The maxim of Quality

try to make your contribution one that is true, specifically:

(i) do not say what you believe to be false

(ii) do not say that for which you lack adequate evidence

The maxim of Quantity

(i) make your contribution as informative as is required for the current purposes of the exchange

(ii) do not make your contribution more informative than is required

The maxim of Relation (or Relevance)

make your contributions relevant

The maxim of Manner

be perspicuous, and specifically:

(i) avoid obscurity

(ii) avoid ambiguity

(iii) be brief (avoid unnecessary prolixity)

(iv) be orderly — Grice (1975:26–27), Levinson (1983:100–102)

Standard implicatures

The simplest situation is where the addressee can draw conclusions from theassumption that the communicator obeys the maxims, as in the following examples. The symbol "+>" means "implicates".[12]

Quality

It is raining. +I believe, and have adequate evidence, that it is raining.

Moore's paradox, the observation that the sentence "It is raining, but I don't believe that it is raining" sounds contradictory although it isn't from a strictly logical point of view, has been explained as a contradiction to this type of implicature. However, as implicatures can be cancelled (see below), this explanation is dubious.[12]

Quantity (i)

A well-known classof quantity implicatures are the scalar implicatures. Prototypical examples include words specifying quantities such as "some", "few", or "many":[13][14]

John ate some of the cookies. +John didn't eat all of the cookies.

Here, the use of "some" semantically entails that more than one cookie was eaten. It does not entail, but implicates, that not every cookie was eaten, or at least that the speaker does not know whether any cookies are left. The reason for this implicature is that saying "some" when one could say "all" would be less than informative enough in most circumstances. The general idea is that the communicator is expected to make the strongest possible claim, implicating the negation of any stronger claim. Lists of expressions that give rise to scalar implicatures, sorted from strong to weak, are known as Horn scales:[13][15]

⟨all, many, some, few⟩

⟨…, four, three, two, one⟩ (cardinal number terms)

⟨always, often, sometimes⟩

⟨and, or⟩

⟨necessarily, possibly⟩

⟨hot, warm⟩

etc.

Negation reverses these scales, as in this example:

She won't necessarily get the job. +She will possibly get the job.

"Not possibly" is stronger than "not necessarily", and the implicature follows from the double negation "She will not [not possibly] get the job".[6]

Here are some further implicatures that can be classified as scalar:[16]

I slept on a boat yesterday. +The boat was not mine.

This is a common construction where the indefinite article indicates that the referent is not closelyassociated with the speaker, because the stronger claim "I slept on my boat yesterday" is not made.[17]

The flag is green. +The flag is completely green.

If this is the strongest possible claim, it follows that the flag has no other features, because "The flag is green and some other colour" would be stronger. In other words, if it did contain other features, this utterance would not be informative enough.[12]

Quantity (ii)

The second quantity maxim seems to work in the opposite direction as the first; the communicator makes a weaker claim, from which a stronger one is implicated. Implicatures arising from this maxim enrich the information contained in the utterance:[18]

He drank a bottle of vodka and fell into a stupor. +He drank a bottle of vodka and consequently fell into a stupor.

I lost a book yesterday. +The book was mine.

There is extensive literature, but no consensus on the question which of the two quantity maxims is in operation in which circumstances; i.e. why "I lost a book yesterday" implicates that the book was the speaker's, while "I slept on a boat yesterday" usually implicates that the boat wasn't the speaker's.[9]

Relation/relevance

That cake looks delicious. +I would like a piece of that cake.

This statement taken by itself would be irrelevant in most situations, so the addressee concludes that the speaker had something more in mind.

The introductory example also belongs here:[3]

A: I am out of gas.

B: There is a gas station 'round the corner. +The gas station is open.

Manner (iv)

The cowboy jumped on his horse and rode into the sunset. +The cowboy performed these two actions in this order.

Being orderly includes relating events in the order they occurred.[12]

Clashes of maxims

Sometimes it is impossible to obey all maxims at once. Suppose that A and B are planning a holiday in France and A suggests they visit their old acquaintance Gérard:

A: Where does Gérard live?

B: Somewhere in the South of France. +B does not know where exactly Gérard lives.

B's answer violates the first maxim of quantity as it does not contain sufficient information to plan their route. But if B does not know the exact location, she cannot obey this maxim and also the maxim of quality; hence the implicature.[19]

Floutings

The maxims can also be blatantly disobeyed or flouted, giving rise to another kind of conversational implicature. This is possible because addressees will go to great lengths in saving theirassumption that the communicator did in fact – perhaps on a deeper level – obey the maxims and the cooperative principle. Many figures of speech can be explained by this mechanism.[20][21]

Quality (i)

Saying something that is obviously false can produce irony, meiosis, hyperbole and metaphor:[20]

When she heard about the rumour, she exploded.

As it is improbable that she really exploded, and it is highly unlikely that the speaker wanted to lie or was simply mistaken, the addressee has to assume the utterance was meant to be metaphorical.

Quantity (i)

Utterances that are not informative on the surface include tautologies. They have no logical content and hence no entailments, but can still be used to convey information via implicatures:[20]

War is war.

Damning with faint praise also works by flouting the first quantity maxim. Consider the following testimonial for a student:

Dear Sir, Mr. X's command of English is excellent, and his attendance at tutorials has been regular. Yours, etc.

The implicature here is that the student is no good, since the teacher has nothing better to say about him.[21]

Relation/relevance

B's answer in the following exchange does not seem to be relevant, so A concludes that B wanted to convey something else:[20]

A: Mrs Jenkins is an old windbag, don't you think?

B: Lovely weather for March, isn't it? +Watch out, her nephew is standing right behind you![22] (or the like)

Manner (iii)

This utterance is much more long-winded than "Miss Singer sang an aria from Rigoletto" and therefore flouts the maxim "Be brief":[20]

Miss Singer produced a series of sounds corresponding closely to the score of an aria from Rigoletto. +What Miss Singer produced cannot really be described as an aria from Rigoletto.

Implicature in relevance theory

Dan Sperber, who developed relevance theory together with Deirdre Wilson

In the framework known as relevance theory, implicature is defined as a counterpart to explicature. The explicatures of an utterance are the communicatedassumptions that are developed from its logical form (intuitively, the literal meaning) by supplying additional information from context: by disambiguating ambiguous expressions,assigning referents to pronouns and other variables, and so on. All communicatedassumptions that cannot be obtained in this way are implicatures.[49][50] For example, if Peter says

Susan told me that her kiwis were too sour.

in the context that Susan participated in a fruit grower's contest, the hearer might arrive at the explicature

Susan told Peter that the kiwifruit she, Susan, grew were too sour for the judges at the fruit grower's contest.

Nowassume that Peter and the hearer both have access to the contextual information that

A presupposition must be mutually known orassumed by the speaker and addressee for the utterance to be considered appropriate in context. It will generally remain a necessaryassumption whether the utterance is placed in the form of anassertion, denial, or question, and can beassociated with a specific lexical item or grammatical feature (presupposition trigger) in the utterance.

Crucially, negation of an expression does not change its presuppositions: I want to do it again and I don't want to do it again both presuppose that the subject has done it already one or more times; My wife is pregnant and My wife is not pregnant both presuppose that the subject has a wife. In this respect, presupposition is distinguished from entailment and implicature. For example, The president wasass2ass==inated entails that The president is dead, but if the expression is negated, the entailment is not necessarily true.

>>15906329

>The president wasass2assinated entails that The president is dead, but if the expression is negated, the entailment is not necessarily true.