Lecture 4 - Michael De
... glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the most natural many-valued extension of classical logic for reasoning ...
... glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the most natural many-valued extension of classical logic for reasoning ...
First-order logic;
... Now use the binomial theorem to compute (1 − (3/4)n−2 )n−1 (1 − (3/4)n−2 )n−1 = 1 − (n − 1)(3/4)n−2 + C (n − 1, 2)(3/4)2(n−2) + · · · For sufficiently large n, this will be (just about) 1. Bottom line: If n is large, then it is almost certain that a random graph will be connected. In fact, with prob ...
... Now use the binomial theorem to compute (1 − (3/4)n−2 )n−1 (1 − (3/4)n−2 )n−1 = 1 − (n − 1)(3/4)n−2 + C (n − 1, 2)(3/4)2(n−2) + · · · For sufficiently large n, this will be (just about) 1. Bottom line: If n is large, then it is almost certain that a random graph will be connected. In fact, with prob ...
pdf
... is, by definition, component (applied) logic'. pragmatic Both ways, the logician can remain at home. As I see it, however, it is never a at far too early for such conclusions. had the Logic good try - and this to is of science devoted the paper theory ground for clearing once said, the important suc ...
... is, by definition, component (applied) logic'. pragmatic Both ways, the logician can remain at home. As I see it, however, it is never a at far too early for such conclusions. had the Logic good try - and this to is of science devoted the paper theory ground for clearing once said, the important suc ...
Intuitionistic Logic
... A ∨ ¬A is indeterminate if A is. But the same will be true of A ∧ ¬A. I can never, however, be in a position to prove both A and ¬A! There are other problems as well; A and ¬¬A will end up equivalent. So, the above considerations do not argue for a many-valued logic. ...
... A ∨ ¬A is indeterminate if A is. But the same will be true of A ∧ ¬A. I can never, however, be in a position to prove both A and ¬A! There are other problems as well; A and ¬¬A will end up equivalent. So, the above considerations do not argue for a many-valued logic. ...
Propositional logic - Computing Science
... To have confidence in the conclusion in your argument, the premises should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for valid arguments? Examples ...
... To have confidence in the conclusion in your argument, the premises should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for valid arguments? Examples ...
Propositional and predicate logic - Computing Science
... To have confidence in the conclusion in your argument, the premises should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for valid arguments? ...
... To have confidence in the conclusion in your argument, the premises should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for valid arguments? ...
RR-01-02
... Event Calculus is the first of a family of other similar definitions, also involving important implementation issues, this assessment result discloses knowledge on how to certify the expressiveness and problem-solving power of these logics. Assuming the given implementation is correct, the final use ...
... Event Calculus is the first of a family of other similar definitions, also involving important implementation issues, this assessment result discloses knowledge on how to certify the expressiveness and problem-solving power of these logics. Assuming the given implementation is correct, the final use ...
Logical Consequence by Patricia Blanchette Basic Question (BQ
... truths that aren’t necessary, which are nevertheless deducible from the empty set , thus violating the modal condition. 2. Show that the rules of inference only have necessary consequences. ...
... truths that aren’t necessary, which are nevertheless deducible from the empty set , thus violating the modal condition. 2. Show that the rules of inference only have necessary consequences. ...
Logic - Disclaimer
... Parentheses and Ambiguity • An ambiguous statements is a statement whose meaning is not clear due to its syntax. Example : ”P or Q and R” • In formal systems, an expression like P Q R is simply not allowed and considered unsyntactical. • Claims in our formal language are therefore never ambiguo ...
... Parentheses and Ambiguity • An ambiguous statements is a statement whose meaning is not clear due to its syntax. Example : ”P or Q and R” • In formal systems, an expression like P Q R is simply not allowed and considered unsyntactical. • Claims in our formal language are therefore never ambiguo ...
What is "formal logic"?
... sections. If we don’t support a logico-formalist philosophy of mathematics, the first three reasons have to be rejected. One central feature of mathematics seems abstraction, but why should abstraction be related to any “formal ontology”? This relation between the abstract and the formal has probabl ...
... sections. If we don’t support a logico-formalist philosophy of mathematics, the first three reasons have to be rejected. One central feature of mathematics seems abstraction, but why should abstraction be related to any “formal ontology”? This relation between the abstract and the formal has probabl ...
Document
... Predicate Logic A predicate of the form P(x1,…,xn), n>1 that states the relationships among the objects x1,…,xn is called polyadic. Also, an n-place predicate or n-ary predicate (a predicate with arity n). ...
... Predicate Logic A predicate of the form P(x1,…,xn), n>1 that states the relationships among the objects x1,…,xn is called polyadic. Also, an n-place predicate or n-ary predicate (a predicate with arity n). ...
Logic is a discipline that studies the principles and methods used in
... Predicate Logic: Existential Quantifier Suppose P(x) is a predicate on some universe of discourse. The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” ∃ x P(x) reads “for some x, P(x)” or “There exists x, P(x) ...
... Predicate Logic: Existential Quantifier Suppose P(x) is a predicate on some universe of discourse. The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” ∃ x P(x) reads “for some x, P(x)” or “There exists x, P(x) ...
Logic
... Parentheses and Ambiguity • An ambiguous statements is a statement whose meaning is not clear due to its syntax. Example : ”P or Q and R” • In formal systems, an expression like P Q R is simply not allowed and considered unsyntactical. • Claims in our formal language are therefore never ambiguo ...
... Parentheses and Ambiguity • An ambiguous statements is a statement whose meaning is not clear due to its syntax. Example : ”P or Q and R” • In formal systems, an expression like P Q R is simply not allowed and considered unsyntactical. • Claims in our formal language are therefore never ambiguo ...
Mathematical Logic Deciding logical consequence Complexity of
... algorithm which takes a polinomial number of steps in n, to determine the validity of A? This is an unsolved problem ...
... algorithm which takes a polinomial number of steps in n, to determine the validity of A? This is an unsolved problem ...
Propositional Logic
... • The program below that I wrote works correctly for all possible inputs….. • The program that I wrote never hangs (i.e. always terminates)… ...
... • The program below that I wrote works correctly for all possible inputs….. • The program that I wrote never hangs (i.e. always terminates)… ...
timeline
... Logicism in the context of the development of set theory I. Grattan-Guinness Set theory began to be developed on a large scale from the late 1890s onwards; for example, it was part of the mathematical logic that grounded logicism, and for convenience much of Principia mathematica was elaborated in i ...
... Logicism in the context of the development of set theory I. Grattan-Guinness Set theory began to be developed on a large scale from the late 1890s onwards; for example, it was part of the mathematical logic that grounded logicism, and for convenience much of Principia mathematica was elaborated in i ...
Curry`s Paradox. An Argument for Trivialism
... the strengthen liar paradox, a paradox originated from the sentence: (a): (a) is not true by holding that (a) is both true and not true. More generally, he holds that the paradoxical sentences obtained from self-reference are dialetheiae. Priest’s dialetheism has been extensively criticized in the l ...
... the strengthen liar paradox, a paradox originated from the sentence: (a): (a) is not true by holding that (a) is both true and not true. More generally, he holds that the paradoxical sentences obtained from self-reference are dialetheiae. Priest’s dialetheism has been extensively criticized in the l ...
Beginning Deductive Logic
... This is rather a deep and tricky question, as of course are relatives like: “What is physics?” and “What is economics?” and “What is art?”. Perhaps one has to be either brave or foolhardy (or both!) to venture an answer to such a question, unless perhaps one has set aside enough time and space to cr ...
... This is rather a deep and tricky question, as of course are relatives like: “What is physics?” and “What is economics?” and “What is art?”. Perhaps one has to be either brave or foolhardy (or both!) to venture an answer to such a question, unless perhaps one has set aside enough time and space to cr ...
ON PRESERVING 1. Introduction The
... transmuted into single formula truth. It may be more correct to say that, but it makes the whole paradigm somewhat less forceful or even less appealing. What we need in order to rescue the very idea of preservationism is to talk entirely about sets. So we shall have to replace the arbitrary conclusi ...
... transmuted into single formula truth. It may be more correct to say that, but it makes the whole paradigm somewhat less forceful or even less appealing. What we need in order to rescue the very idea of preservationism is to talk entirely about sets. So we shall have to replace the arbitrary conclusi ...
LCD_5
... The OR gate has two or more inputs and single output. The output of OR gate is HIGH only when any one of its inputs are HIGH (i.e. even if one input is HIGH, Output will be HIGH). If X and Y are two inputs, then output F can be represented mathematically as F = X+Y. Here plus sign (+) denotes ...
... The OR gate has two or more inputs and single output. The output of OR gate is HIGH only when any one of its inputs are HIGH (i.e. even if one input is HIGH, Output will be HIGH). If X and Y are two inputs, then output F can be represented mathematically as F = X+Y. Here plus sign (+) denotes ...
MATH 4110: Advanced Logic
... An excellent student has a clear comprehension of the details of an intricate, non‐trivial mathema cal result: the completeness of first‐order logic with iden ty. They can give a clear and comprehensive outline of the major steps in the proof using their own words and without notes. They have a clea ...
... An excellent student has a clear comprehension of the details of an intricate, non‐trivial mathema cal result: the completeness of first‐order logic with iden ty. They can give a clear and comprehensive outline of the major steps in the proof using their own words and without notes. They have a clea ...
In Defence of Indispensability
... standard ZFC axioms. The two- competing axiom candidates are Godel's axiom of constructibility, V = L, and some large cardinal axiom, such as MC (there exists a measurable cardinal). These two candidates both settle the question at hand, but with different answers. MC implies that all Ej sets are Le ...
... standard ZFC axioms. The two- competing axiom candidates are Godel's axiom of constructibility, V = L, and some large cardinal axiom, such as MC (there exists a measurable cardinal). These two candidates both settle the question at hand, but with different answers. MC implies that all Ej sets are Le ...
PARADOX AND INTUITION
... cannot force the interpretation of any of its predicate-letters as a relation with a nondenumerable field. Some connections between the Löwenheim-Skolem theorem and problems of ontological reduction are discussed in Quine 1966. It has been stressed there that in the proof of the Löwenheim-Skolem the ...
... cannot force the interpretation of any of its predicate-letters as a relation with a nondenumerable field. Some connections between the Löwenheim-Skolem theorem and problems of ontological reduction are discussed in Quine 1966. It has been stressed there that in the proof of the Löwenheim-Skolem the ...
03_Artificial_Intelligence-PredicateLogic
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
Modal_Logics_Eyal_Ariel_151107
... Let be a set of propositions. These propositions describe facts about the system as “the system is deadlocked” or “the value of variable x is 5”. An interpreted system is a tuple (S,V), where ...
... Let be a set of propositions. These propositions describe facts about the system as “the system is deadlocked” or “the value of variable x is 5”. An interpreted system is a tuple (S,V), where ...
Willard Van Orman Quine
Willard Van Orman Quine (/kwaɪn/; June 25, 1908 – December 25, 2000) (known to intimates as ""Van"") was an American philosopher and logician in the analytic tradition, recognized as ""one of the most influential philosophers of the twentieth century."" From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978. A recent poll conducted among analytic philosophers named Quine as the fifth most important philosopher of the past two centuries. He won the first Schock Prize in Logic and Philosophy in 1993 for ""his systematical and penetrating discussions of how learning of language and communication are based on socially available evidence and of the consequences of this for theories on knowledge and linguistic meaning."" In 1996 he was awarded the Kyoto Prize in Arts and Philosophy for his ""outstanding contributions to the progress of philosophy in the 20th century by proposing numerous theories based on keen insights in logic, epistemology, philosophy of science and philosophy of language.""Quine falls squarely into the analytic philosophy tradition while also being the main proponent of the view that philosophy is not conceptual analysis but the abstract branch of the empirical sciences. His major writings include ""Two Dogmas of Empiricism"" (1951), which attacked the distinction between analytic and synthetic propositions and advocated a form of semantic holism, and Word and Object (1960), which further developed these positions and introduced Quine's famous indeterminacy of translation thesis, advocating a behaviorist theory of meaning. He also developed an influential naturalized epistemology that tried to provide ""an improved scientific explanation of how we have developed elaborate scientific theories on the basis of meager sensory input."" He is also important in philosophy of science for his ""systematic attempt to understand science from within the resources of science itself"" and for his conception of philosophy as continuous with science. This led to his famous quip that ""philosophy of science is philosophy enough."" In philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the ""Quine–Putnam indispensability thesis,"" an argument for the reality of mathematical entities.