x - WordPress.com
... humans. Human beings make decisions based on rules. Although, we may not be aware of it, all the decisions we make are all based on computer like if-then statements. If the weather is fine, then we may decide to go out. If the forecast stays the weather will be bad today, but fine tomorrow, then we ...
... humans. Human beings make decisions based on rules. Although, we may not be aware of it, all the decisions we make are all based on computer like if-then statements. If the weather is fine, then we may decide to go out. If the forecast stays the weather will be bad today, but fine tomorrow, then we ...
Propositional logic
... Definition: a set of wffs S logically implies a wff a, S |= a, provided that for each assignment s such that s(b) = T for each bŒS, s(a) = T (if S = ∅, write |= a and a is a tautology). ...
... Definition: a set of wffs S logically implies a wff a, S |= a, provided that for each assignment s such that s(b) = T for each bŒS, s(a) = T (if S = ∅, write |= a and a is a tautology). ...
PROVING UNPROVABILITY IN SOME NORMAL MODAL LOGIC
... Now, let T = < W, R > be an arbitrarily fixed tree with a set of nodes W = {x1 , . . . , xn }. We attach to these nodes different propositional variables q(x1 ), . . . , q(xn ) or for V short q1 , . . . , qn . This set will be referred as var(T ). Denote χ(xi ) = qi ∧ {¬qj : qj ∈ var(T ), j 6= i}. N ...
... Now, let T = < W, R > be an arbitrarily fixed tree with a set of nodes W = {x1 , . . . , xn }. We attach to these nodes different propositional variables q(x1 ), . . . , q(xn ) or for V short q1 , . . . , qn . This set will be referred as var(T ). Denote χ(xi ) = qi ∧ {¬qj : qj ∈ var(T ), j 6= i}. N ...
Chapter1_Parts2
... Solution: Construct the truth table for the proposition. Then an equivalent proposition is the disjunction with n disjuncts (where n is the number of rows for which the formula evaluates to T). Each disjunct has m conjuncts where m is the number of distinct propositional variables. Each conjunct inc ...
... Solution: Construct the truth table for the proposition. Then an equivalent proposition is the disjunction with n disjuncts (where n is the number of rows for which the formula evaluates to T). Each disjunct has m conjuncts where m is the number of distinct propositional variables. Each conjunct inc ...
Lecture Notes in Computer Science
... proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only of theoretical significance, but also bears upon computational issues. It was one purpos ...
... proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only of theoretical significance, but also bears upon computational issues. It was one purpos ...
PDF
... † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
... † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
Tautologies Arguments Logical Implication
... This is (yet another) hot area of computer science. • How do you prove that your program is correct? – You could test it on a bunch of instances. That runs the risk of not exercising all the features of the program. In general, this is an intractable problem. • For small program fragments, formal ve ...
... This is (yet another) hot area of computer science. • How do you prove that your program is correct? – You could test it on a bunch of instances. That runs the risk of not exercising all the features of the program. In general, this is an intractable problem. • For small program fragments, formal ve ...
MathsReview
... R is “less than equal to” () For S = {1, 2, 3} Example of R on S is {(1, 1), (1, 2), (1, 3), ????) ...
... R is “less than equal to” () For S = {1, 2, 3} Example of R on S is {(1, 1), (1, 2), (1, 3), ????) ...
Notes
... Do we know that any inhabited OCaml SL specification is “true” in mathematics? This can be shown in a strong sense as our examples suggest. We’ll examine this below. Do we know that any specification we could write down in mathematics or logic can be expressed as an OCaml SL specification? What abou ...
... Do we know that any inhabited OCaml SL specification is “true” in mathematics? This can be shown in a strong sense as our examples suggest. We’ll examine this below. Do we know that any specification we could write down in mathematics or logic can be expressed as an OCaml SL specification? What abou ...
.pdf
... enters into some true proposition, and the substitution of Q for P wherever it appears results in a new proposition that is likewise true, and if this can be done for every proposition, then P and Q are said to be the same and conversely, if P and Q are the same, they can be substituted for one an ...
... enters into some true proposition, and the substitution of Q for P wherever it appears results in a new proposition that is likewise true, and if this can be done for every proposition, then P and Q are said to be the same and conversely, if P and Q are the same, they can be substituted for one an ...
1. Axioms and rules of inference for propositional logic. Suppose T
... For Ass, Ex, Contr and Cut this amounts to the so called “generalized rules of inference” on stated and proved on pp. 91-93 of the coursepack. The rest are a straightforward exercise for the reader making use of associativity. ...
... For Ass, Ex, Contr and Cut this amounts to the so called “generalized rules of inference” on stated and proved on pp. 91-93 of the coursepack. The rest are a straightforward exercise for the reader making use of associativity. ...
Theories.Axioms,Rules of Inference
... axioms. (Axioms are theorems.) When we start ACL2, it has lots of functions already defined and it correspondingly has axioms for those functions in its theory. Remember from the Lecture 5 that some functions are “primitive” and some are “derived?” The axioms governing derived functions come from th ...
... axioms. (Axioms are theorems.) When we start ACL2, it has lots of functions already defined and it correspondingly has axioms for those functions in its theory. Remember from the Lecture 5 that some functions are “primitive” and some are “derived?” The axioms governing derived functions come from th ...
pdf - Consequently.org
... These do not match: the inference rules are sound for the models, but not complete, so either the proof rules are too weak or the models are too strong. Some, such as Quine, take this to be no real problem, since they take “second order logic” to be a misnomer. It is not logic but set theory in shee ...
... These do not match: the inference rules are sound for the models, but not complete, so either the proof rules are too weak or the models are too strong. Some, such as Quine, take this to be no real problem, since they take “second order logic” to be a misnomer. It is not logic but set theory in shee ...
Chapter 1: The Foundations: Logic and Proofs
... that is neither a tautology nor a contradiction. ...
... that is neither a tautology nor a contradiction. ...
Lecture 3.1
... R is “less than equal to” () For S = {1, 2, 3} Example of R on S is {(1, 1), (1, 2), (1, 3), ????) ...
... R is “less than equal to” () For S = {1, 2, 3} Example of R on S is {(1, 1), (1, 2), (1, 3), ????) ...
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.