In formal semantics, a Hurford disjunction is a disjunction in which one of the disjuncts entails the other. The concept was first identified by British linguist James Hurford. [1] The sentence "Mary is in the Netherlands or she is in Amsterdam" is an example of a Hurford disjunction since one cannot be in Amsterdam without being in the Netherlands. Other examples are shown below: [2] [3]
- #Tamina saw a Beatle or Paul McCartney.
- #The number I'm thinking of is divisible by 4 or it's even.
- #Is Wilbur a pig or an animal?
As indicated by the octothorps in the above examples, Hurford disjunctions are typically infelicitous. Their infelicity has been argued to arise from them being redundant, since simply uttering the stronger of the two disjuncts would have had the same semantic effect. Thus, they have been taken as motivation for a principle such as the following: [3] [4]
- Local Redundancy: An utterance is infelicitous if its logical form contains an instance of a binary operator
applied to arguments 
or 
, whose semantic contribution is contextually equivalent to that of either or on its own.
However, some particular instances of Hurford disjunctions are felicitous. [2] [5]
- Sofia ate some of the pizza or all of it.
- Henrietta is five feet tall or six feet tall.
Felicitous Hurford disjunctions have been analyzed by positing that the weaker disjunct is strengthened by an embedded scalar implicature which eliminates the entailment between the disjuncts. For instance, in the first of the felicitous examples above, the left disjunct's unenriched meaning is simply that Sofia ate a nonzero amount of pizza. This would result in a redundancy violation since eating all the pizza entails eating a nonzero amount of it. However, if an embedded scalar implicature enriches this disjunct so that it denotes the proposition that that Sofia ate some but not all of the pizza, this entailment no longer goes through. Eating all of the pizza does not entail eating some but not all of it. Thus, Local Redundancy will still be satisfied. [2] [5]
In logic, disjunction is a logical connective typically notated whose meaning either refines or corresponds to that of natural language expressions such as "or". In classical logic, it is given a truth functional semantics on which is true unless both and are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an inclusive interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well the numerous mismatches between classical disjunction and its nearest equivalents in natural language.
In propositional logic, disjunction elimination, is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It is the inference that if a statement implies a statement and a statement also implies , then if either or is true, then has to be true. The reasoning is simple: since at least one of the statements P and R is true, and since either of them would be sufficient to entail Q, Q is certainly true.
In logic, a logical connective is a logical constant used to connect two or more formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions.
In linguistics and related fields, pragmatics is the study of how context contributes to meaning. Pragmatics encompasses phenomena including implicature, speech acts, relevance and conversation. Theories of pragmatics go hand-in-hand with theories of semantics, which studies aspects of meaning which are grammatically or lexically encoded. The ability to understand another speaker's intended meaning is called pragmatic competence. Pragmatics emerged as its own subfield in the 1950s after the pioneering work of J.L. Austin and Paul Grice.
Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ.
Herbert Paul Grice, usually publishing under the name H. P. Grice, H. Paul Grice, or Paul Grice, was a British philosopher of language. He is best known for his theory of implicature and the cooperative principle, which became foundational concepts in the linguistic field of pragmatics. His work on meaning has also influenced the philosophical study of semantics.
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. 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". Take for example the following exchange:
Linguistic entailments are entailments which arise in natural language. If a sentence A entails a sentence B, sentence A cannot be true without B being true as well. For instance, the English sentence "Pat is a fluffy cat" entails the sentence "Pat is a cat" since one cannot be a fluffy cat without being a cat. On the other hand, this sentence does not entail "Pat chases mice" since it is possible for a cat to not chase mice.
Counterfactual conditionals are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives, which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of fake tense morphology, which some languages use in combination with other kinds of morphology including aspect and mood.
The material conditional is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum.
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 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 pragmatics, scalar implicature, or quantity implicature, is an implicature that attributes an implicit meaning beyond the explicit or literal meaning of an utterance, and which suggests that the utterer had a reason for not using a more informative or stronger term on the same scale. The choice of the weaker characterization suggests that, as far as the speaker knows, none of the stronger characterizations in the scale holds. This is commonly seen in the use of 'some' to suggest the meaning 'not all', even though 'some' is logically consistent with 'all'. If Bill says 'I have some of my money in cash', this utterance suggests to a hearer that Bill does not have all his money in cash.
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.
A bare noun is a noun that is used without a surface determiner or quantifier. In natural languages, the distribution of bare nouns is subject to various language-specific constraints. Under the DP hypothesis a noun in an argument position must have a determiner or quantifier that introduces the noun, warranting special treatment of the bare nouns that seemingly contradict this. As a result, bare nouns have attracted extensive study in the fields of both semantics and syntax.
Inquisitive semantics is a framework in logic and natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and the issue that it raises. The framework provides a foundation for the linguistic analysis of statements and questions. It was originally developed by Ivano Ciardelli, Jeroen Groenendijk, Salvador Mascarenhas, and Floris Roelofsen.
Free choice is a phenomenon in natural language where a disjunction appears to receive a conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie and that they can also play video games, depending on their preference.
- You can watch a movie or play video games.
- You can watch a movie or you can play video games.
In formal semantics, the squiggle operator is an operator which constrains the occurrence of focus. On one common definition, the squiggle operator takes a syntactic argument and a discourse salient argument and introduces a presupposition that the ordinary semantic value of is either a subset or an element of the focus semantic value of . The squiggle was first introduced by Mats Rooth in 1992 as part of his treatment of focus within the framework of alternative semantics. It has become one of the standard tools in formal work on focus, playing a key role in accounts of contrastive focus, ellipsis, deaccenting, and question-answer congruence.
In linguistics, a subsective modifier is an expression which modifies another by delivering a subset of its denotation. For instance, the English adjective "skilled" is subsective since being a skilled surgeon entails being a surgeon. By contrast, the English adjective "alleged" is non-subsective since an "alleged spy" need not be an actual spy.
In formal semantics and philosophical logic, simplification of disjunctive antecedents (SDA) is the phenomenon whereby a disjunction in the antecedent of a conditional appears to distribute over the conditional as a whole. This inference is shown schematically below:
