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  2. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    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.

  3. Predicate (grammar) - Wikipedia

    en.wikipedia.org/wiki/Predicate_(grammar)

    Predicates may also be collective or distributive. Collective predicates require their subjects to be somehow plural, while distributive ones do not. An example of a collective predicate is "formed a line". This predicate can only stand in a nexus with a plural subject: The students formed a line. — Collective predicate appears with plural ...

  4. List of first-order theories - Wikipedia

    en.wikipedia.org/wiki/List_of_first-order_theories

    List or describe a set of sentences in the language L σ, called the axioms of the theory. Give a set of σ-structures, and define a theory to be the set of sentences in L σ holding in all these models. For example, the "theory of finite fields" consists of all sentences in the language of fields that are true in all finite fields. An L σ ...

  5. Predicate (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Predicate_(mathematical_logic)

    A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.

  6. Predicative expression - Wikipedia

    en.wikipedia.org/wiki/Predicative_expression

    A predicative expression (or just predicative) is part of a clause predicate, and is an expression that typically follows a copula or linking verb, e.g. be, seem, appear, or that appears as a second complement of a certain type of verb, e.g. call, make, name, etc. [1] The most frequently acknowledged types of predicative expressions are predicative adjectives (also predicate adjectives) and ...

  7. Glossary of logic - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_logic

    For example, in arithmetic, addition and multiplication are associative. asymmetry A relation between two entities where if the first is related to the second, the second is not related to the first. atomic formula The simplest type of formula in logic, consisting of a single predicate applied to a sequence of terms without any logical connectives.

  8. Theta role - Wikipedia

    en.wikipedia.org/wiki/Theta_role

    The number and category are indicated by a feature called ARG-STR. This feature is an ordered list of categories that must cooccur with a particular verb or predicate. For example, the ARG-STR list of the verb give is <NP, NP, PP>. The semantic part of theta roles (i.e. the thematic relations) are treated in a special set of semantic ...

  9. Sentence (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Sentence_(mathematical_logic)

    The following example in first-order logic (=) is a sentence. This sentence means that for every y, there is an x such that =. This sentence is true for positive real numbers, false for real numbers, and true for complex numbers. However, the formula