In logic, disjunction is a logical connective typically notated as and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula , assuming that abbreviates "it is sunny" and abbreviates "it is warm".
In logic, a logical connective is a logical constant. They can be used to connect logical 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 .
A proposition is a central concept in semantics, logic, philosophy of language and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves linguistic expressions. For instance, the English sentence "Snow is white" denotes the same proposition as the German sentence "Schnee ist weiß" even though the two sentences are not the same. Similarly, propositions can also be characterized as the objects of belief and other propositional attitudes. For instance if one believes that the sky is blue, what one believes is the proposition that the sky is blue. A proposition can also be thought of as a kind of idea: Collins Dictionary has a definition for proposition as "a statement or an idea that people can consider or discuss whether it is true."
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
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.
Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models. Montague pioneered this approach in the 1960s and early 1970s.
Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and semantic composition, since it typically treats syntactic categories as corresponding to semantic types. Categorial grammars were developed in the 1930s by Kazimierz Ajdukiewicz and in the 1950s by Yehoshua Bar-Hillel and Joachim Lambek. It saw a surge of interest in the 1970s following the work of Richard Montague, whose Montague grammar assumed a similar view of syntax. It continues to be a major paradigm, particularly within formal semantics.
Donkey sentences are sentences that contain a pronoun with clear meaning but whose syntactical role in the sentence poses challenges to grammarians. Such sentences defy straightforward attempts to generate their formal language equivalents. The difficulty is with understanding how English speakers parse such sentences.
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.
Gennaro Chierchia is an Italian linguist and educator. Chierchia is currently the Haas Foundation Professor of Linguistics and Professor of Philosophy at Harvard University. His work and study focus on areas including semantics, pragmatics, philosophy of language, and language pathology.
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.
Formal semantics is the study of grammatical meaning in natural languages using formal tools 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.
Lauri Juhani Karttunen was an adjunct professor in linguistics at Stanford and an ACL Fellow. He died in 2022.
Craige Roberts is an American linguist, known for her work on pragmatics and formal semantics.
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 linguistic disjunction appears to receive a logical 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 that constrains the occurrence of focus. In 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 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. 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:
- #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?
The Temperature Paradox or Partee's Paradox is a classic puzzle in formal semantics and philosophical logic. Formulated by Barbara Partee in the 1970s, it consists of the following argument, which speakers of English judge as wildly invalid.
- The temperature is ninety.
- The temperature is rising.
- Therefore, ninety is rising.
In linguistics exhaustivity refers to an implicature in which a proposition is strengthened by denying its stronger alternatives. It is a major topic in the linguistic subfields of semantics and pragmatics.
