Order Logic

Some articles on logic, order logic, logics:

BIT Predicate
... In mathematical logic, the BIT predicate, sometimes written BIT(i, j), is a predicate which tests whether the jth bit of the number i is 1, when i is written in binary ... We can also prove that the class FO + BIT, of first-order logic with the BIT predicate, is the same as the class FO + PLUS + TIMES, of first-order logic with addition and ...
Stewart Shapiro - Publications - Papers
... the mathematician", Current Issues in Logic / Temas Actuales de Lógica ... The limits of logic", introduction to The limits of logic Second order logic and the Skolem paradox, The international research library of philosophy (see above), Dartmouth Publishing Company ... "The triumph of first order logic", Festschrift for Alonzo Church, University of Chicago Press, forthcoming ...
Theory (mathematical Logic) - Theories Expressed in Formal Language Generally - Consistency and Completeness
... In a deductive system (such as first-order logic) that satisfies the principle of explosion, this is equivalent to requiring that there is no sentence φ such that both φ and its negation can be proven ... For first-order logic, the most important case, it follows from the completeness theorem that the two meanings coincide ... In other logics, such as second-order logic, there are syntactically consistent theories that are not satisfiable, such as ω-inconsistent theories ...
Ancestral Relation - Discussion
... Principia Mathematica made repeated use of the ancestral, as does Quine's (1951) Mathematical Logic ... noting that the ancestral relation cannot be defined in first-order logic, and following the resolution of Russell's paradox both Frege and Quine largely considered the use of ... In particular, Quine did not consider second-order logic to be "logic" at all, despite his reliance upon it for his 1951 book (which largely retells ...
Logicus - Topics in Logic - Predicate Logic
... Predicate logic is the generic term for symbolic formal systems such as first-order logic, second-order logic, many-sorted logic, and infinitary logic ... Predicate logic provides an account of quantifiers general enough to express a wide set of arguments occurring in natural language ... Aristotelian syllogistic logic specifies a small number of forms that the relevant part of the involved judgements may take ...

Famous quotes containing the words logic and/or order:

    The usefulness of madmen is famous: they demonstrate society’s logic flagrantly carried out down to its last scrimshaw scrap.
    Cynthia Ozick (b. 1928)

    ...I feel anxious for the fate of our monarchy, or democracy, or whatever is to take place. I soon get lost in a labyrinth of perplexities; but, whatever occurs, may justice and righteousness be the stability of our times, and order arise out of confusion. Great difficulties may be surmounted by patience and perseverance.
    Abigail Adams (1744–1818)