User:Phlsph7/Formal semantics - Studied linguistic phenomena

Studied linguistic phenomena

Reference, Generalized quantifiers, Indefinites, Plurality, Genericity, Tense, Aspect, Mereology, Vagueness, Modification, Negation, Conditionals, Modality, Questions, Imperatives(Aloni 2016 chapters)
i/p, truth cond, models & sets, context, fragment of english, type theory, lambda, quantification, inference, time/tense, aspect (imperfect/perfect/continuous), intensionality(Cann 1993)
worlds, situations, nouns, noun phrases, properties, kinds (Bach 1989)
intentional states (BORG 2004)
type theory (Chatzikyriakidis 2020)
quantification, binding, reference/deixis, intensionality, model theory, context(Keenan 1975)
noun phrase, pragmatics, dynamic, tense, aspect, modality, conjunction, type-shifting, questions, negative polarity(Portner 2002 intro)
pred, modifiers, ref, quantifier, intensionality, tense/aspect/modality, prop att, pragmatics(Portner 2005)
prop att (Vanderveken 2011)
meaning, form, entailment, Intensionality and Possible Worlds, De dicto/de re, functions for linguistic denotations, monotonicity, anaphora, DEFINITE AND INDEFINITE DESCRIPTIONS, plural, tense & aspect, q & imp (Winter 2016)
- "(i) entailment as an empirical phenomenon revealing important aspects of meaning (ii) the compositionality principle as a bridge between meaning and form"(Winter 2016)
structural ambiguity (winter 2016 pp. 30–31)
examples of problematic sentences to translate^[1]

Generalized quantifiers

Quantifiers are expressions that indicate the quantity of something. The most basic quantifiers in predicate logic only provide information about whether a condition applies to all or some entities, as in sentences like "all ravens are black" and "some students smoke". Formal semanticists use the concept of generalized quantifiers to extend this basic framework to a broad range quantificational expressions in natural language that usually provide more detailed information. They include diverse types, such as most, few, twelve, and fewer than ten.^[2]^[3]^[4]

Most quantificational expressions can be interpreted as relations between two sets.^[a] For instance, the sentence "all ravens are black" expresses the idea that the set of ravens is a subset of the set of black beings. Similarly, the sentence "fewer than ten books were sold" asserts that the set of books and the set of sold items have fewer than ten elements in common.^[2]^[6]^[7] In English, quantifiers are often expressed with a determiner,^[b] such as all and few, indicating the relation between the sets, followed by a noun phrase and a verb phrase^{[citation needed]} to describe the involved sets.^[8]^[9]^[7]

Quantifiers can be divided into proportional and cardinal quantifiers based on the type of relation between the sets. Proportional quantifiers, such as all and most, indicate the relative overlap of the first set with the second set. For them, the order of the sets matters. For instance, the sentences "all ravens are black" and "all black things are ravens" have different meanings even though they refer to the same sets of things. Cardinal quantifiers, such as four and no, provide information about the absolute number of overlapping entities independent of the relative proportion. For them, the order of the sets does not matter, as exemplified by the sentences "no rose is black" and "no black thing is a rose".^[3]^[2]

Typically, the domain of natural language quantifiers is implicitly limited to a certain range of entities relevant to the discussed issue. For example, in the context of a specific kindergarten, the domain of sentence "all children are sleeping" is limited to the children attending this kindergarten. ^[10]^[11]^[12]

The scope of a quantifier is the part of the sentence to which it applies. Some natural language sentences have scope ambiguity, meaning that there are competing interpretations about the scope of quantifiers. Depending on how scope is interpreted, the sentence "Some man loves every woman" can mean either "there is a man such that he loves all women" or "for every woman there is at least one man who loves her".^[13]

Definite and indefinite descriptions

Definite and indefinite descriptions are phrases that denote a specific entity within a given context. Definite descriptions are typically expressed with definite article the, followed by a noun phrase, such as "the president of Kenya", but can also take other forms, such as "her husband" and "John's bicycle". Indefinite descriptions are usually expressed with the indefinite articles a and an, as in an employee and a friend of Mary's.^[14]^[15]^[16] Definite descriptions usually assume that the listener can identify the referent, whereas indefinite descriptions introduce an entity without presupposing prior knowledge.^{[citation needed]}

Diverse theories about the correct analysis of definite and indefinite descriptions have been proposed. An influential view, suggested by Bertrand Russell, interprets them as existential quantifiers. For him, indefinite descriptions like "a man danced" have the logical form $\exists x(Man(x)\land Danced(x))$ . Definite description have a similar form with the only difference that the description is unique, meaning that the first predicate only applies to a single entity.^[17] A central motivation for Russell's approach was to solve semantic puzzles that arise from definite descriptions that do not refer any particular entity. For example, the sentence "the present king of France is bald" refers to a non-existing entity, resulting in difficulties when trying to determine its meaning and truth value. According to Russell's analysis, the sentence is false, since no unique entity exists to which the predicates "present king of France" and "bald" applies.^[18]^[19]^[20]

The problem of names is closely related to that of definite descriptions since both expressions aim to refer to a particular entity. According to Millian theories, names refer directly without any descriptive information of the denotated entity. This view is rejected by description theories, which argue that names carry implicit descriptive contents that help interpreters identify their referents. One view understands names as implicit definite descriptions, proposing, for example, that the descriptive content of the name Socrates may include information like "the teacher of Plato and Xenophon".^[21]^[22]^[23]^[24]

Tense, aspect, and events

Tense and aspect provide temporal information about events and circumstances. Tense indicates whether something happened in the past, present, or future, offering a reference point to place events within a timeline relative to the time of the utterance. Aspect conveys additional information about how events unfold in time, like the distinction between completed, ongoing, and repetitive events. In English, both tense and aspect can be expressed through verb forms. On the level of tense the sentence "I ate" indicates the past while the sentence "I will eat" indicates the future. On the level of aspect, the sentence "I ate" indicates a completed action whereas the sentence "I was eating" indicates an ongoing action.^[25]^[26]^[27]

Formal semanticists employ diverse conceptual tools to describe tense, such as temporal logic, which extends predicate logic. One form of temporal logic introduces tense operators to indicate which time a sentence describes, like the the operator $P$ for past events and the operator $F$ for future events. This way, the formula $PDances(naomi)$ expresses that Naomi danced in the past, while $FDances(naomi)$ asserts that she will dance in the future. Another approach is to modify predicates with an additional slot^{[citation needed]} to indicate the time when they happened. This way, the formula $Dances(naomi,t_{1})$ states that Naomi danced at the time $t_{1}$ .^[28]^[29]^[30]

For example, the sentence "I ate" describes an action in the past on the level of tense that was completed on the level of aspect. Similarly, the sentence "I am eating" expresses an action in the present on the level of tense that is ongoing on the level of aspect.

Intensionality, modality, and propositional attitudes

Extensional vs. Intensional Contexts
de dicto vs de re

Questions and imperatives

Others

negation
anaphora and pronouns
plurals and mass terms
indexicality and deixis

References

Notes

^ In type theory, sets can be interpreted as characteristic functions from enities to truth values of the type $\langle e,t\rangle$ , returning true if the entity is a member of the set and false otherwise. As a consequence, most quantifiers have the type $\langle \langle e,t\rangle ,\langle \langle e,t\rangle ,t\rangle \rangle$ , corresponding to a function that takes two sets as inputs and outputs a truth value that depends on the relation between the sets.^[2]^[5]
^ In some cases, bare plurals act as quantifiers without a determiner, such as the sentence "firemen wear helmets", expressing the idea that all firemen wear helmets.^[8]

Citations

^ Fox 2014, pp. 88.
^ ^a ^b ^c ^d Westerståhl 2016, pp. 206–209.
^ ^a ^b Kearns 2011, pp. 94–97.
^ Portner 2005, pp. 112–114.
^ Kearns 2011, pp. 121–122.
^ Kearns 2011, pp. 96–98.
^ ^a ^b Winter 2016, pp. 114–118.
^ ^a ^b Westerståhl 2016, pp. 210–211.
^ Kearns 2011, pp. 97–98.
^ Iacona 2015, p. 130.
^ Westerståhl 2016, pp. 212–213.
^ Kearns 2011, pp. 106–107.
^ Kearns 2011, p. 105.
^ Ostertag 2009, pp. 194–195.
^ Ludlow 2023, Lead section, § 1. What are Descriptions?.
^ Winter 2016, pp. 235.
^ Ludlow 2023, § 2. Russell's Theory of Descriptions.
^ Kearns 2011, pp. 111–113.
^ Ostertag 2009, pp. 195–196.
^ Ludlow 2023, § 3. Motivations for Russell's Theory of Descriptions, § 5.1 The challenge to Russell's truth conditions.
^ Reimer 2009, pp. 762–763.
^ Ludlow 2023, § 4.1 Descriptive theories of proper names.
^ Cumming 2023, § 2.1 Meaning and Extension.
^ Kearns 2011, pp. 111–112.
^ Kearns 2011, pp. 176–177.
^ Winter 2016, pp. 235–236.
^ Portner 2005, pp. 137–138.
^ Kearns 2011, pp. 185–188.
^ Portner 2005, pp. 139–141.
^ Goranko & Rumberg 2025, § 3. Prior's basic tense logic TL.

Sources

Westerståhl, Dag (2016). "7. Generalized Quantifiers". In Aloni, Maria; Dekker, Paul (eds.). The Cambridge Handbook of Formal Semantics. Cambridge University Press. pp. 206–237. ISBN 978-1-316-55273-5.
Iacona, Andrea (2015). "Quantification and Logical Form". In Torza, Alessandro (ed.). Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language. Springer. ISBN 978-3-319-18362-6.
Ludlow, Peter (2023). "Descriptions". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 2 June 2025.
Ostertag, G. (2009). "Definite and Indefinite Descriptions". In Allan, Keith (ed.). Concise Encyclopedia of Semantics. Elsevier. pp. 194–200. ISBN 978-0-08-095969-6.
Cumming, Sam (2023). "Names". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 2 June 2025.
Reimer, M. (2009). "Proper Names: Philosophical Aspects". In Allan, Keith (ed.). Concise Encyclopedia of Semantics. Elsevier. pp. 762–766. ISBN 978-0-08-095969-6.
Goranko, Valentin; Rumberg, Antje (2025). "Temporal Logic". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 2 June 2025.

[6] In type theory, sets can be interpreted as characteristic functions from enities to truth values of the type $\langle e,t\rangle$ , returning true if the entity is a member of the set and false otherwise. As a consequence, most quantifiers have the type $\langle \langle e,t\rangle ,\langle \langle e,t\rangle ,t\rangle \rangle$ , corresponding to a function that takes two sets as inputs and outputs a truth value that depends on the relation between the sets.^[2]^[5]

[10] In some cases, bare plurals act as quantifiers without a determiner, such as the sentence "firemen wear helmets", expressing the idea that all firemen wear helmets.^[8]

[FOOTNOTEFox201488-1] Fox 2014, pp. 88.

[FOOTNOTEWesterståhl2016206–209-2] Westerståhl 2016, pp. 206–209.

[FOOTNOTEKearns201194–97-3] Kearns 2011, pp. 94–97.

[FOOTNOTEPortner2005[httpsbooksgooglecombooksidorYpEQAAQBAJpgPA112_112–114]-4] Portner 2005, pp. 112–114.

[FOOTNOTEKearns2011121–122-5] Kearns 2011, pp. 121–122.

[FOOTNOTEKearns201196–98-7] Kearns 2011, pp. 96–98.

[FOOTNOTEWinter2016114–118-8] Winter 2016, pp. 114–118.

[FOOTNOTEWesterståhl2016210–211-9] Westerståhl 2016, pp. 210–211.

[FOOTNOTEKearns201197–98-11] Kearns 2011, pp. 97–98.

[FOOTNOTEIacona2015[httpsbooksgooglecombooksidyR4_CgAAQBAJpgPA130_130]-12] Iacona 2015, p. 130.

[FOOTNOTEWesterståhl2016212–213-13] Westerståhl 2016, pp. 212–213.

[FOOTNOTEKearns2011106–107-14] Kearns 2011, pp. 106–107.

[FOOTNOTEKearns2011105-15] Kearns 2011, p. 105.

[FOOTNOTEOstertag2009194–195-16] Ostertag 2009, pp. 194–195.

[FOOTNOTELudlow2023Lead_section,_§_1._What_are_Descriptions?-17] Ludlow 2023, Lead section, § 1. What are Descriptions?.

[FOOTNOTEWinter2016235-18] Winter 2016, pp. 235.

[FOOTNOTELudlow2023§_2._Russell's_Theory_of_Descriptions-19] Ludlow 2023, § 2. Russell's Theory of Descriptions.

[FOOTNOTEKearns2011111–113-20] Kearns 2011, pp. 111–113.

[FOOTNOTEOstertag2009195–196-21] Ostertag 2009, pp. 195–196.

[FOOTNOTELudlow2023§_3._Motivations_for_Russell's_Theory_of_Descriptions,_§_5.1_The_challenge_to_Russell's_truth_conditions-22] Ludlow 2023, § 3. Motivations for Russell's Theory of Descriptions, § 5.1 The challenge to Russell's truth conditions.

[FOOTNOTEReimer2009762–763-23] Reimer 2009, pp. 762–763.

[FOOTNOTELudlow2023§_4.1_Descriptive_theories_of_proper_names-24] Ludlow 2023, § 4.1 Descriptive theories of proper names.

[FOOTNOTECumming2023§_2.1_Meaning_and_Extension-25] Cumming 2023, § 2.1 Meaning and Extension.

[FOOTNOTEKearns2011111–112-26] Kearns 2011, pp. 111–112.

[FOOTNOTEKearns2011176–177-27] Kearns 2011, pp. 176–177.

[FOOTNOTEWinter2016235–236-28] Winter 2016, pp. 235–236.

[FOOTNOTEPortner2005137–138-29] Portner 2005, pp. 137–138.

[FOOTNOTEKearns2011185–188-30] Kearns 2011, pp. 185–188.

[FOOTNOTEPortner2005139–141-31] Portner 2005, pp. 139–141.

[FOOTNOTEGorankoRumberg2025§_3._Prior's_basic_tense_logic_TL-32] Goranko & Rumberg 2025, § 3. Prior's basic tense logic TL.

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