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Topic: Propositional logic

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	PlanetMath: propositional logic (Site not responding. Last check: 2007-11-07)
		A propositional logic is a logic in which the only objects are propositions, that is, objects which themselves have truth values.
		Propositional logic is decidable: there is an easy way to determine whether a sentence is a tautology.
		This is version 3 of propositional logic, born on 2002-09-26, modified 2002-09-28.
	www.planetmath.org /encyclopedia/PropositionalLogic.html (235 words)

	Logical Fallacy: Fallacy of Propositional Logic
		Propositional logic is a system which deals with the logical relations that hold between propositions taken as a whole, and those compound propositions which are constructed from simpler ones with truth-functional connectives.
		Moreover, the connective "and" which joins them is truth-functional, that is, the truth-value of the compound proposition is a function of the truth-values of its components.
		Propositional logic studies the logical relations which hold between propositions as a result of truth-functional combinations, for instance, the example conjunction implies "today is Sunday".
	www.fallacyfiles.org /propfall.html (303 words)

	Propositional logic - Wikipedia, the free encyclopedia
		In mathematical logic, propositional logic is the logic of mathematical objects called propositions.
		The language of a propositional calculus consists of (1) a set of primitive symbols, variously referred to as atomic formulas, placeholders, proposition letters, or variables, and (2) a set of operator symbols, variously interpreted as logical operators or logical connectives.
		When the "atomic sentences" of propositional logic are broken up into terms, variables, predicates, and quantifiers, they yield first-order logic, or first-order predicate logic, which keeps all the rules of propositional logic and adds some new ones.
	en.wikipedia.org /wiki/Propositional_logic (3306 words)

	Propositional Logic [Internet Encyclopedia of Philosophy]
		Propositional logic, also known as sentential logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements.
		In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement.
		However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another.
	www.iep.utm.edu /p/prop-log.htm (8796 words)

	COT 3100 Topic 1: Fundamentals of Logic (Site not responding. Last check: 2007-11-07)
		Understanding how to use propositional logic is a generally useful tool for thought, because it allows you to extend your innate logical reasoning abilities to the realm of long, complex ideas.
		Predicate logic is logic language that includes propositional logic, and additionally adds the ability to precisely express statements that are explicitly about particular objects, all objects, or some objects of a given class.
		Predicate logic has widespread applications in all areas of mathematics and theoretical computer science (for precisely expressing and proving complex statements), in program verification (proving that programs or parts of programs are correct in all cases), and in some database query languages and advanced programming languages.
	www.cise.ufl.edu /~mpf/logic.html (592 words)

	Wff, Propositional Logic (Site not responding. Last check: 2007-11-07)
		Propositional logic is a formal system for performing and studying this kind of reasoning.
		Propositional logic does not "know" if it is raining or not, whether `raining' is true or false.
		A study of propositional logic is basic to a study of these fields.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Wff (1922 words)

	Propositional logic (Site not responding. Last check: 2007-11-07)
		Propositional logic, also known as sentential logic, is the branch of logic...
		The Calculus of Structures - Modal Logics Several normal propositional modal logics are systematically presented in the calculus of structures and cut elimination is proved.
		Propositional Attitude Reports Explores semantic accounts of propositional attitude reports, and some of the theories developed to deal with Frege's puzzle.
	www.serebella.com /encyclopedia/article-Propositional_logic.html (1449 words)

	Propositional Logic Applet
		Propositional logic uses true statements to form or prove other true statements.
		A proposition is satisfiable it is true for at least one interpretation G. Example: p is satisfiable since p is true for G(p)=1
		This theorem is the basis of reasoning in propositional logic.
	www.oursland.net /aima/propositionApplet.html (906 words)

	Intuitionistic Logic
		Philosophically, intuitionism differs from logicism by treating logic as a part of mathematics rather than as the foundation of mathematics; from finitism by allowing (constructive) reasoning about infinite collections; and from platonism by viewing mathematical objects as mental constructs with no independent ideal existence.
		While identity can of course be added to intuitionistic logic, for applications (e.g., to arithmetic) the equality symbol is generally treated as a distinguished predicate constant satisfying nonlogical axioms (e.g., the primitive recursive definitions of addition and multiplication) in addition to reflexivity, symmetry and transitivity.
		Propositional Kripke semantics is particulary simple, since an arbitrary propositional formula is intuitionistically provable if and only if it is forced by the root of every Kripke model whose frame (the set K of nodes together with their partial ordering) is a finite tree with a least element (the root).
	plato.stanford.edu /entries/logic-intuitionistic (6042 words)

	Propositional Logic (Site not responding. Last check: 2007-11-07)
		Propositional logic is a mathematical model (or algebra) for reasoning about the truth of logical expressions (propositions).
		Logical expressions can be manipulated according to algebraic laws, allowing us to reason formally (using deductive reasoning) about a set of premises.
		Although propositional logic is powerful enough to be used in these many different contexts, like any formal system, there are limits to its applicability.
	www.cs.rochester.edu /~nelson/courses/csc_173/proplogic (101 words)

	Propositional Logic (Site not responding. Last check: 2007-11-07)
		Propositional variables (whose value is TRUE or FALSE) and the propositional constants TRUE and FALSE are logical expressions.
		The meaning (or value) of a logical expression is a Boolean function from the set of possible assignments of truth values for the variables in the expression to the values {TRUE,FALSE}.
		A tautology is a logical expression that is always TRUE, regardless of the assignment of truth values to the variables in the expressions.
	www.cs.rochester.edu /u/leblanc/csc173/proplogic/expressions.html (1815 words)

	CITIDEL: Viewing 'propositional logic' (Site not responding. Last check: 2007-11-07)
		propositional logic is a logic in which the only objects are...
		Variables represent propositions, and there are no relations, functions, or quantifiers except for the constants T and bot (representing true and false respectively).
		A model for propositional logic is just a truth function nu on a set of variables.
	www.citidel.org /?op=getobj&identifier=oai:PlanetMath:PropositionalLogic (232 words)

	Fuzzy Logic
		Saying “yes” (which is the mainstream of fuzzy logic) one accepts the truth-functional approach; this makes fuzzy logic to something distinctly different from probability theory since the latter is not truth-functional (the probability of conjunction of two propositions is not determined by the probabilities of those propositions).
		Fuzzy logic in the narrow sense is symbolic logic with a comparative notion of truth developed fully in the spirit of classical logic (syntax, semantics, axiomatization, truth-preserving deduction, completeness, etc.; both propositional and predicate logic).
		This fuzzy logic is a relatively young discipline, both serving as a foundation for the fuzzy logic in a broad sense and of independent logical interest, since it turns out that strictly logical investigation of this kind of logical calculi can go rather far.
	plato.stanford.edu /entries/logic-fuzzy (2595 words)

	Introduction to Logic (Site not responding. Last check: 2007-11-07)
		The foundation of the logic we are going to learn here was laid down by a British mathematician George Boole in the middle of the 19th century, and it was further developed and used in an attempt to derive all of mathematics by Gottlob Frege, a German mathematician, towards the end of the 19th century.
		In logic we are interested in true or false of statements, and how the truth/falsehood of a statement can be determined from other statements.
		There are various types of logic such as logic of sentences (propositional logic), logic of objects (predicate logic), logic involving uncertainties, logic dealing with fuzziness, temporal logic etc. Here we are going to be concerned with propositional logic and predicate logic, which are fundamental to all types of logic.
	www.cs.odu.edu /~toida/nerzic/content/logic/intr_to_logic.html (262 words)

	COMPUTABILITY LOGIC: a theory of interactive computation HOMEPAGE
		Technically CL is a game logic: it understands interactive computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems.
		The name "universal" is related to the potential of this logic to integrate, on the basis of one semantics, classical, intuitionistic and linear logics, with their seemingly unrelated or even antagonistic philosophies.
		The inherent incompleteness of affine or linear logics, resulting from the fundamental limitations of the underlying sequent-calculus approach, is apparently the reason why such intuitions and examples, while so heavily relied on in the popular linear-logic literature, have never really found a good explication in the form of a mathematically strict and intuitively convincing semantics.
	www.cis.upenn.edu /~giorgi/cl.html (4288 words)

	prop1
		Thus the truth-value of a proposition is its truth or falsity.
		is a compound proposition whose truth-value depends on the truth-value of it component propositions.
		A negation is a compound truth-functional proposition because it is the denial of a claim.
	www.olemiss.edu /courses/logic/prop1.htm (538 words)

	syllogistic vs. propositional logic (Site not responding. Last check: 2007-11-07)
		Propositional logic, the logic of simple statements, developed mostly in the late 19th and early 20th centuries following Boole's attempts to express mathematical laws of thought.
		It is more mathematical and exact than syllogistic and rhetorical logic, so it's used in electronics, computer science, and to some extent in mathematics, and philosophy.
		Predicate logic is the generalized and mathematical version of syllogistic logic.
	www.welltrainedmind.com /HSboard3/messages/3826.html (279 words)

	propositional logic from FOLDOC (Site not responding. Last check: 2007-11-07)
		Such a logic concerns elementary propositions - p, q, r, s, etc. -- respecting which the only assumption is that they should individually be either true or false, and operators that form complex propositons when joined with appropriate numbers of elementary propositons.
		This logic is concerned with determining which complex propositions are logical truths, or tautologies; this effectively determines what are valid arguments because such can always be treated as complex propositions in which the premisses} of the argument appear as the antecedent and the conclusion as the consequence.
		This logic, as opposed to first, or higher, order predicate logic is complete and decidable.
	www.swif.uniba.it /lei/foldop/foldoc.cgi?propositional+logic (168 words)

	Kautz 1996: Pushing the envelope: planning propositional logic, and stochastic search
		Planning as stochastic search (Walksat) in the space of propositional SAT problems (as opposed to the traditional view of planning as systematic search in the state space or the space of partial plans).
		This is a straightforward simplification of the propositional sentence using standard logic inference rules such as unit propagation, subsumption and deletion of unit clauses.
		This is possible because the corresponding structure is abstracted away in a near-linear logical sentence.
	www.cc.gatech.edu /~jimmyd/summaries/kautz1996.html (650 words)

	Propositional Logic Applet
		Propositional Logic (unquantified logic): Copi's treatment of propositional logic begins with a 50-page chapter explaining connectives and equivalence (including de Morgan's theorems).
		The introduction of the ideas of predicate logic and quantification is good, but there is no discussion of relational predicates.
		A compound statement (compound proposition) is one with two or more simple statements as parts or what we will call components.
	www.wu.ece.ufl.edu /books/CS/TheoreticalCS/logic.html (1382 words)

	Book
		The central problem of propositional logic is whether there is a proof system in which every tautology has a proof of size polynomial in the size of the tautology.
		Bounded arithmetic and propositional logic are closely interrelated and have several explicit and implicit connections to the computational complexity theory around the {\em $P$ versus $NP$} problem.
		The last several years have seen important developments in areas of complexity theory, as well as in bounded arithmetic and complexity of propositional logic, and other deep relations between these areas were established.
	www.math.cas.cz /~krajicek/kniha-obsah.html (731 words)

	The Propositional Logic Calculator
		The only limitation for this calculator is that you have only three atomic propositions to choose from: p,q and r.
		You can use the propositional atoms p,q and r, the "NOT" operatior (for negation), the "AND" operator (for conjunction), the "OR" operator (for disjunction), the "IMPLIES" operator (for implication), and the "IFF" operator (for bi-implication), and the parentheses to state the precedence of the operators.
		The truth value assignments for the propositional atoms p,q and r are denoted by a sequence of 0 and 1.
	www.cs.man.ac.uk /~franconi/teaching/propcalc (288 words)

	Formal Specification of Propositional Logic in ML
		This is a very simple formal specification of the version of propositional logic called PS by Hunter in [Hunter71].
		The system is a classical propositional logic with two connectives (not and implies) presented as a "Hilbert style" axiom system in which there is just one inference rule, modus ponens, and three axiom schemata.
		An interpretation is a map assigning to each propositional variable one of the two truth values true and false.
	www.rbjones.com /rbjpub/logic/log018.htm (455 words)

	Propositional Logic. Mathematical Logic. Part 2.
		On the algebra of logic: A contribution to the philosophy of notation.
		This theorem provides a kind of a "constructive embedding" for the classical propositional logic: any classically provable formula can be "proved" in the constructive logic, if you put two negations before it.
		But, then, we are forced to define the constructive propositional logic not as a subset of the classical one, but as the classical logic with the axiom ~~B->B replaced by the "crazy" axiom L
	www.ltn.lv /~podnieks/mlog/ml2.htm (4408 words)

	prop2 (Site not responding. Last check: 2007-11-07)
		P is a sufficient condition for Q. Q is a necessary condition for P. We will be using a different (and easier!) method for constructing truth-tables than the one used in your text.
		Everytime we add another simple proposition (or letter symbolizing such a proposition) the number of possible combinations of T and F doubles, and thus so do the number of rows in the truth-table.
		After constructing the possible truth-value (the columns) simply fill in the spaces underneath the appropriate truth-functional operators, being careful to follow the rules for such operators as defined by their truth-tables (see last handout).
	www.olemiss.edu /courses/logic/prop2.htm (275 words)

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