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Homogeneity (linguistics)
In formal semantics (natural language), formal semantics, homogeneity is the phenomenon where plural expressions that seem to mean "all" negate to "none" rather than "not all". For example, the English language, English sentence "Robin read the books" requires Robin to have read all of the books, while "Robin didn't read the books" requires her to have read none of them. Neither sentence is true if she read exactly half of the books. Homogeneity effects have been observed in a variety of languages including Japanese language, Japanese, Russian language, Russian, and Hungarian language, Hungarian. Semanticists have proposed a variety of explanations for homogeneity, often involving a combination of presupposition, plural quantification, and trivalent logics. Because analogous effects have been observed with conditional sentence, conditionals and other Modality (linguistics), modal expressions, some semanticists have proposed that these phenomena involve pluralities of possible worlds. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Semantics (natural Language)
Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic 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. Overview Formal semantics studies the denotations of natural language expressions. High-level concerns include compositionality, reference, and the nature of meaning. Key topic areas include scope, modality, binding, tense, and aspect. Semantics is distinct from pragmatics, which encompasses aspects of meaning which arise from interaction and communicative intent. Formal semantics is an interdisciplinary field, often viewed as a subfield of both linguistics and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective \lor can be used to join the two atomic formulas P and Q, rendering the complex formula P \lor Q . Common connectives include negation, disjunction, conjunction, and implication. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classical compositional se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and computer science. History In English, the study of meaning in language has been known by many names that involve the Ancient Greek word (''sema'', "sign, mark, token"). In 1690, a Greek rendering of the term ''semiotics'', the interpretation of signs and symbols, finds an early allusion in John Locke's ''An Essay Concerning Human Understanding'': The third Branch may be called [''simeiotikí'', "semiotics"], or the Doctrine of Signs, the most usual whereof being words, it is aptly enough termed also , Logick. In 1831, the term is suggested for the third branch of division of knowledge akin to Locke; the "signs of our knowledge". In 1857, the term '' semasiology'' (borrowed from German ''Semasiologie'') is attested in Josiah W. Gibbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trivalent Logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminate third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for ''true'' and ''false''. Emil Leon Post is credited with first introducing additional logical truth degrees in his 1921 theory of elementary propositions. The conceptual form and basic ideas of three-valued logic were initially published by Jan Łukasiewicz and Clarence Irving Lewis. These were then re-formulated by Grigore Constantin Moisil in an axiomatic algebraic form, and also extended to ''n''-valued logics in 1945. Pre-discovery Around 1910, Charles Sanders Peirce defined a many-valued logic system. He never published it. In fact, he did not even number the three pages of notes where h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predication (philosophy)
Predication in philosophy refers to an act of judgement where one term is subsumed under another. A comprehensive conceptualization describes it as the understanding of the relation expressed by a predicative structure primordially (i.e. both originally and primarily) through the opposition between particular and general or the one and the many. Predication is also associated or used interchangeably with the concept of ''attribution'' where both terms pertain to the way judgment and ideas acquire a new property in the second operation of the mind (or the mental operation of judging). Background Predication emerged when ancient philosophers began exploring reality and the two entities that divide it: properties and the things that bear them. These thinkers investigated what the division between thing and property amounted to. It was argued that the relationship resembled the logical analysis of a sentence wherein the division of subject and predicate arises spontaneously. It w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Excluded Middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradiction, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law (or principle) of the excluded third, in Latin ''principium tertii exclusi''. Another Latin designation for this law is ''tertium non datur'': "no third ossibilityis given". It is a tautology. The principle should not be confused with the semantical principle of bivalence, which states that every proposition is either true or false. The principle of bivalence always implies the law of excluded middle, while the converse is not always true. A commonly cited counterexample uses statements unprovable now, but provable in the future ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulativity (linguistics)
In linguistic semantics, an expression X is said to have cumulative reference if and only if the following holds: If X is true of both of ''a'' and ''b'', then it is also true of the combination of ''a'' and ''b''. Example: If two separate entities can be said to be "water", then combining them into one entity will yield more "water". If two separate entities can be said to be "a house", their combination cannot be said to be "a house". Hence, "water" has cumulative reference, while the expression "a house" does not. The plural form "houses", however, ''does'' have cumulative reference. If two (groups of) entities are both "houses", then their combination will still be "houses". Cumulativity has proven relevant to the linguistic treatment of the mass/count distinction and for the characterization of grammatical telicity. Formally, a cumulative predicate ''CUM'' can be defined as follows, where capital ''X'' is a variable over sets, ''U'' is the universe of discourse, ''p'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Choice Inference
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. Free choice inferences are a major topic of research in formal semantics and philosophical logic because they are not valid in classical systems of modal logic. If they were valid, then the semantics of natural language would validate the ''Free Choice Principle''. # ''Free Choice Principle'': (\Diamond P \lor \Diamond Q) \rightarrow (\Diamond P \land \Diamond Q) This symbolic logic formula above is not valid in classical modal logic: Adding this principle as an axiom to standard modal logics would allow one to conclude \D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Possible World
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status has been a subject of controversy in philosophy, with modal realists such as David Lewis arguing that they are literally existing alternate realities, and others such as Robert Stalnaker arguing that they are not. Logic Possible worlds are one of the foundational concepts in modal and intensional logics. Formulas in these logics are used to represent statements about what ''might'' be true, what ''should'' be true, what one ''believes'' to be true and so forth. To give these statements a formal interpretation, logicians use structures containing possible worlds. For instance, in the relational semantics for classical propositional modal logic, the formula \Diamond P (read as "possibly P") is actually true if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type (computer Science)
In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers), characters and Booleans. A data type constrains the possible values that an expression, such as a variable or a function, might take. This data type defines the operations that can be done on the data, the meaning of the data, and the way values of that type can be stored. Concept A data type is a collection or grouping of data values. Such a grouping may be defined for many reasons: similarity, convenience, or to focus the attention. It is frequently a matter of good organization that aids the understanding of complex definitions. Almost all programming languages explicitly include the notion of data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vagueness
In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is not vague since every number is definitively either prime or not. Vagueness is commonly diagnosed by a predicate's ability to give rise to the Sorites paradox. Vagueness is separate from ambiguity, in which an expression has multiple denotations. For instance the word "bank" is ambiguous since it can refer either to a river bank or to a financial institution, but there are no borderline cases between both interpretations. Vagueness is a major topic of research in philosophical logic, where it serves as a potential challenge to classical logic. Work in formal semantics has sought to provide a compositional semantics for vague expressions in natural language. Work in philosophy of language has addressed implications of vagueness for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Choice Inference
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. Free choice inferences are a major topic of research in formal semantics and philosophical logic because they are not valid in classical systems of modal logic. If they were valid, then the semantics of natural language would validate the ''Free Choice Principle''. # ''Free Choice Principle'': (\Diamond P \lor \Diamond Q) \rightarrow (\Diamond P \land \Diamond Q) This symbolic logic formula above is not valid in classical modal logic: Adding this principle as an axiom to standard modal logics would allow one to conclude \D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
