First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all men are mortal", in first-order logic one can have expressions in the form "for all x, if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "... is a man" and "... is mortal" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
In linguistics and grammar, a pronoun is a word or a group of words that one may substitute for a noun or noun phrase.
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. The idea is related to a placeholder, or a wildcard character that stands for an unspecified symbol.
In philosophy and logic, a deflationary theory of truth is one of a family of theories that all have in common the claim that assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement.
In linguistics, anaphora is the use of an expression whose interpretation depends upon another expression in context. In a narrower sense, anaphora is the use of an expression that depends specifically upon an antecedent expression and thus is contrasted with cataphora, which is the use of an expression that depends upon a postcedent expression. The anaphoric (referring) term is called an anaphor. For example, in the sentence Sally arrived, but nobody saw her, the pronoun her is an anaphor, referring back to the antecedent Sally. In the sentence Before her arrival, nobody saw Sally, the pronoun her refers forward to the postcedent Sally, so her is now a cataphor. Usually, an anaphoric expression is a pro-form or some other kind of deictic expression. Both anaphora and cataphora are species of endophora, referring to something mentioned elsewhere in a dialog or text.
In linguistics, focus is a grammatical category that conveys which part of the sentence contributes new, non-derivable, or contrastive information. In the English sentence "Mary only insulted BILL", focus is expressed prosodically by a pitch accent on "Bill" which identifies him as the only person whom Mary insulted. By contrast, in the sentence "Mary only INSULTED Bill", the verb "insult" is focused and thus expresses that Mary performed no other actions towards Bill. Focus is a cross-linguistic phenomenon and a major topic in linguistics. Research on focus spans numerous subfields including phonetics, syntax, semantics, pragmatics, and sociolinguistics.
In linguistics, coreference, sometimes written co-reference, occurs when two or more expressions refer to the same person or thing; they have the same referent. For example, in Bill said Alice would arrive soon, and she did, the words Alice and she refer to the same person.
In generative grammar and related frameworks, a node in a parse tree c-commands its sister node and all of its sister's descendants. In these frameworks, c-command plays a central role in defining and constraining operations such as syntactic movement, binding, and scope. Tanya Reinhart introduced c-command in 1976 as a key component of her theory of anaphora. The term is short for "constituent command".
In generative grammar and related approaches, the logical form (LF) of a linguistic expression is the variant of its syntactic structure which undergoes semantic interpretation. It is distinguished from phonetic form, the structure which corresponds to a sentence's pronunciation. These separate representations are postulated in order to explain the ways in which an expression's meaning can be partially independent of its pronunciation, e.g. scope ambiguities.
Attempto Controlled English (ACE) is a controlled natural language, i.e. a subset of standard English with a restricted syntax and restricted semantics described by a small set of construction and interpretation rules. It has been under development at the University of Zurich since 1995. In 2013, ACE version 6.7 was announced.
In semantics, a donkey sentence is a sentence containing a pronoun which is semantically bound but syntactically free. They are a classic puzzle in formal semantics and philosophy of language because they are fully grammatical and yet defy straightforward attempts to generate their formal language equivalents. In order to explain how speakers are able to understand them, semanticists have proposed a variety of formalisms including systems of dynamic semantics such as Discourse representation theory. Their name comes from the example sentence "Every farmer who owns a donkey beats it", in which "it" acts as a donkey pronoun because it is semantically but not syntactically bound by the indefinite noun phrase "a donkey". The phenomenon is known as donkey anaphora.
Quantificational variability effect (QVE) is the intuitive equivalence of certain sentences with quantificational adverbs (Q-adverbs) and sentences without these, but with quantificational determiner phrases (DP) in argument position instead.
Johan Anthony Willem "Hans" Kamp is a Dutch philosopher and linguist, responsible for introducing discourse representation theory (DRT) in 1981.
A bound variable pronoun is a pronoun that has a quantified determiner phrase (DP) – such as every, some, or who – as its antecedent.
Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dynamic semantics, knowing the meaning of a sentence means knowing "the change it brings about in the information state of anyone who accepts the news conveyed by it." In dynamic semantics, sentences are mapped to functions called context change potentials, which take an input context and return an output context. Dynamic semantics was originally developed by Irene Heim and Hans Kamp in 1981 to model anaphora, but has since been applied widely to phenomena including presupposition, plurals, questions, discourse relations, and modality.
Logophoricity is a phenomenon of binding relation that may employ a morphologically different set of anaphoric forms, in the context where the referent is an entity whose speech, thoughts, or feelings are being reported. This entity may or may not be distant from the discourse, but the referent must reside in a clause external to the one in which the logophor resides. The specially-formed anaphors that are morphologically distinct from the typical pronouns of a language are known as logophoric pronouns, originally coined by the linguist Claude Hagège. The linguistic importance of logophoricity is its capability to do away with ambiguity as to who is being referred to. A crucial element of logophoricity is the logophoric context, defined as the environment where use of logophoric pronouns is possible. Several syntactic and semantic accounts have been suggested. While some languages may not be purely logophoric, logophoric context may still be found in those languages; in those cases, it is common to find that in the place where logophoric pronouns would typically occur, non-clause-bounded reflexive pronouns appear instead.
Formal semantics is the study of grammatical meaning in natural languages using formal concepts from logic, mathematics and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse-engineering the semantic components of natural languages' grammars.
Noun ellipsis (N-ellipsis), also noun phrase ellipsis (NPE), is a mechanism that elides, or appears to elide, part of a noun phrase that can be recovered from context. The mechanism occurs in many languages like English, which uses it less than related languages.
In linguistics, givenness is a phenomenon in which a speaker assumes that contextual information of a topic of discourse is already known to the listener. The speaker thus considers it unnecessary to supply further contextual information through an expression's linguistic properties, its syntactic form or position, or its patterns of stress and intonation. Givenness involves contextual information in a discourse that is given, or assumed to be known, by the addressee in the moment of utterance. Therefore, a given expression must be known from prior discourse.
In formal semantics, the scope of a semantic operator is the semantic object to which it applies. For instance, in the sentence "Paulina doesn't drink beer but she does drink wine," the proposition that Paulina drinks beer occurs within the scope of negation, but the proposition that Paulina drinks wine does not. Scope can be thought of as the semantic order of operations.
