For more on the reduction of second-order logic to many-sorted logic, we refer to Manzano (1996).
For detailed discussion of specific fields, see the articles applied logic, formal logic, modal logic, and logic, philosophy of.
Independence friendly logic (IF logic, IF first-order logic) is an extension of first-order logic.
In addition to deductive logic, there are other branches of logic that study inferences based on notions such as knowing that (epistemic logic), believing that (doxastic logic), time (tense logic), and moral obligation (deontic logic), among others.
actualism | Aristotle, General Topics: logic | existence | generalized quantifiers | logic: classical | logic: free | logic: intuitionistic | logic: modal | logic: second-order and higher-order | model theory | plural quantification | square of opposition
Whereas (first order) dependence logic is strictly more expressive than first order logic, propositional dependence logic is not more expressive than propositional logic, as it follows immediately from the fact that all propositional functions are expressible in propositional logic.
category theory | God, arguments for the existence of: moral arguments | Hume, David: moral philosophy | logic: algebraic propositional | logic: classical | logic: deontic | logic: intuitionistic | logic: many-valued | logic: modal | logic: paraconsistent | logic: temporal | logical consequence
compositionality | logic: and games | logic: dependence | logic: independence friendly | logic: infinitary | logic: intuitionistic | logic: temporal | meaning, theories of | model theory | model theory: first-order | Tarski, Alfred | truth | truth: axiomatic theories of | truth: deflationary theory of | truth: revision theory of
dialetheism | Gödel, Kurt: incompleteness theorems | lambda calculus, the | liar paradox | logic: algebraic propositional | logic: combinatory | logic: linear | logic: paraconsistent | logic: substructural | negation | paradoxes: and contemporary logic | Russell’s paradox | self-reference | set theory: alternative axiomatic theories
game theory | generalized quantifiers | logic: classical | logic: dialogical | logic: epistemic | logic: for analyzing games | logic: independence friendly | logic: infinitary | logic: informal | logic: intuitionistic | logic: linear | logic: modal | model theory | set theory
compositionality | game theory | generalized quantifiers | logic: and games | logic: classical | logic: dependence | logic: dialogical | logic: epistemic | logic: intensional | logic: intuitionistic | logic: modal | logic: second-order and higher-order | model theory | reasoning: automated | set theory | Tarski, Alfred: truth definitions
actualism | algebra of logic tradition | Boolean algebra: the mathematics of | logic: algebraic propositional | logic: classical | logic: deontic | logic: hybrid | logic: intensional | logic: many-valued | logic: modal | logic: relevance | logic: temporal | modality: medieval theories of | possible objects | possible worlds | Prior, Arthur
logic: free | logic: infinitary | logic: intuitionistic | logic: linear | logic: modal | logic: paraconsistent | logic: relevance | logic: second-order and higher-order | logic: substructural | logic: temporal | logical consequence | logical form | logical truth | model theory | model theory: first-order | paradox: Skolem’s | proof theory: development of
algebra | category theory | computability and complexity | Curry’s paradox | Gödel, Kurt | lambda calculus, the | logic, history of: intuitionistic logic | logic: intuitionistic | logic: linear | logic: relevance | logic: second-order and higher-order | logic: substructural | proof theory: development of | Quine, Willard Van Orman | reasoning: automated | recursive functions | Russell’s paradox | type theory | type theory: Church’s type theory
Aristotle, General Topics: logic | Bolzano, Bernard | Carnap, Rudolf | Frege, Gottlob: theorem and foundations for arithmetic | logic, normative status of | logic: algebraic propositional | logic: classical | logic: inductive | logic: intuitionistic | logic: non-monotonic | logic: substructural | logical constants | logical form | logical pluralism | logical truth | model theory | proof theory | Russell, Bertrand | schema | semantics: proof-theoretic
category theory | connectives: sentence connectives in formal logic | Curry’s paradox | Hilbert, David: program in the foundations of mathematics | logic, history of: intuitionistic logic | logic: classical | logic: intuitionistic | logic: linear | logic: substructural | logical constants | mathematics, philosophy of: intuitionism | paradoxes: and contemporary logic | proof theory: development of | realism: challenges to metaphysical | Russell’s paradox | self-reference | truth: revision theory of | type theory
artificial intelligence: logic and | computability and complexity | Curry’s paradox | Fitch’s paradox of knowability | Gödel, Kurt | Gödel, Kurt: incompleteness theorems | Hilbert, David: program in the foundations of mathematics | logic, history of: modal logic | logic: classical | logic: epistemic | logic: intuitionistic | logic: modal | logic: relevance | mathematics: constructive | model theory | possible worlds | Principia Mathematica | proof theory: development of | Quine, Willard Van Orman | self-reference | set theory: independence and large cardinals | Turing, Alan
decision theory | epistemology: Bayesian | games: abstraction and completeness | game theory | game theory: epistemic foundations of | game theory: evolutionary | learning theory, formal | logic: and games | logic: and probability | logic: conditionals | logic: deontic | logic: dependence | logic: dynamic epistemic | logic: epistemic | logic: for analyzing power in normal form games | logic: independence friendly | logic: justification | logic: modal | logic: propositional dynamic | logic: temporal | probability, interpretations of | social procedures, formal approaches
abduction | actualism | agency | common knowledge | computational complexity theory | epistemic paradoxes | epistemology | epistemology: social | game theory: epistemic foundations of | indexicals | intention | knowledge: analysis of | logic: action | logic: classical | logic: combining | logic: deontic | logic: dynamic epistemic | logic: epistemic | logic: justification | logic: modal | logic: of belief revision | logic: propositional dynamic | logic: temporal | model theory: first-order | Peirce, Charles Sanders | possible worlds | quantifiers and quantification | questions | Russell’s paradox | self-reference | semantics: two-dimensional
actualism | artificial intelligence: logic and | category theory | choice, axiom of | descriptions | epsilon calculus | Frege, Gottlob | Gödel, Kurt: incompleteness theorems | grammar: typelogical | lambda calculus, the | logic, history of: first-order logic | logic: classical | logic: deontic | logic: dynamic epistemic | logic: modal | logic: second-order and higher-order | metaphysics | ontological arguments | paradox: Skolem’s | paradoxes: and contemporary logic | possible worlds | Principia Mathematica | proof theory | quantifiers and quantification | Quine, Willard Van Orman | rational choice, normative: expected utility | reasoning: automated | Russell, Bertrand | semantics: Montague | Tarski, Alfred | type theory
Logic
noun cognition
- the branch of philosophy that analyzes inference
noun cognition
- reasoned and reasonable judgment
Example: it made a certain kind of logic
noun cognition
- the principles that guide reasoning within a given field or situation
Example: economic logic requires it
noun cognition
- the system of operations performed by a computer that underlies the machine's representation of logical operations
noun cognition
- a system of reasoning
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actualism | artificial intelligence logic and | category theory | choice axiom of | descriptions | epsilon calculus | Frege Gottlob | Gödel Kurt incompleteness theorems | grammar typelogical | lambda calculus the | logic history of first-order logic | logic classical | logic deontic | logic dynamic epistemic | logic modal | logic second-order and higher-order | metaphysics | ontological arguments | paradox Skolems | paradoxes and contemporary logic | possible worlds | Principia Mathematica | proof theory | quantifiers and quantification | Quine Willard Van Orman | rational choice normative expected utility | reasoning automated | Russell Bertrand | semantics Montague | Tarski Alfred | type theory