Chapter 2
... Objectives: Analyze statements in if-then form Write the converse, inverse and contrapositive of if-then statements Vocabulary: Implies symbol (→) Conditional statement – statement written in if-then form Hypothesis – phrase immediately following the word if in a conditional statement Conclusion – p ...
... Objectives: Analyze statements in if-then form Write the converse, inverse and contrapositive of if-then statements Vocabulary: Implies symbol (→) Conditional statement – statement written in if-then form Hypothesis – phrase immediately following the word if in a conditional statement Conclusion – p ...
Identity in modal logic theorem proving
... and methods are applications of what it is legal to do within the proof theory. (In Whitehead ~ Russell, this amounts to finding substitution instances of formulas for propositional variables in the axioms, and applying Modus Ponens). Were one directly constructing proofs in Smullyan [14] tableaux s ...
... and methods are applications of what it is legal to do within the proof theory. (In Whitehead ~ Russell, this amounts to finding substitution instances of formulas for propositional variables in the axioms, and applying Modus Ponens). Were one directly constructing proofs in Smullyan [14] tableaux s ...
Transfinite progressions: A second look at completeness.
... to give an updated version of Feferman’s completeness result partly based on later developments, aiming to clarify the argument rather than include every detail. Second, to answer the natural non-technical question just what it is about reflection principles that makes it possible to prove, by iterat ...
... to give an updated version of Feferman’s completeness result partly based on later developments, aiming to clarify the argument rather than include every detail. Second, to answer the natural non-technical question just what it is about reflection principles that makes it possible to prove, by iterat ...
Mathematics: the divine madness
... ”There is, strictly, no such thing as mathematical proof: we can, in the last analysis, do nothing but point. Proofs are what Littlewood and I call ’gas’: —rhetorical flourishes designed to affect psychology, pictures on board in the lecture, —devices to stimulate the imagination of pupils.” —A Math ...
... ”There is, strictly, no such thing as mathematical proof: we can, in the last analysis, do nothing but point. Proofs are what Littlewood and I call ’gas’: —rhetorical flourishes designed to affect psychology, pictures on board in the lecture, —devices to stimulate the imagination of pupils.” —A Math ...
on partially conservative sentences and interpretability
... every \¡i e F. In §1 this concept for T - 2°+, and Tl°+, is investigated. In §2 results from §1 are applied to interpretability in theories containing arithmetic. ...
... every \¡i e F. In §1 this concept for T - 2°+, and Tl°+, is investigated. In §2 results from §1 are applied to interpretability in theories containing arithmetic. ...
doc - Brown CS
... Determining whether a given Boolean expression is satisfiable is NP-complete, and thus if P NP, cannot be done in polynomial time by a deterministic machine. Suppose however, instead of trying to determine whether an arbitrary Boolean expression is satisfiable, we only we only want to determine wh ...
... Determining whether a given Boolean expression is satisfiable is NP-complete, and thus if P NP, cannot be done in polynomial time by a deterministic machine. Suppose however, instead of trying to determine whether an arbitrary Boolean expression is satisfiable, we only we only want to determine wh ...
Chapter 5 Predicate Logic
... f (H) = {hm, mi, hm, ni, hm, Ni, hn, ni, hn, Ni, hN, Ni}. We can use this latter interpretation of H to treat another predicate logic formula: (∀x)H(x, x). Here there is still only one quantifier and no connectives, but there is more than one quantified variable. The interpretation is that both argu ...
... f (H) = {hm, mi, hm, ni, hm, Ni, hn, ni, hn, Ni, hN, Ni}. We can use this latter interpretation of H to treat another predicate logic formula: (∀x)H(x, x). Here there is still only one quantifier and no connectives, but there is more than one quantified variable. The interpretation is that both argu ...
![Propositions as [Types] - Research Showcase @ CMU](http://s1.studyres.com/store/data/005730189_1-e85fa7d3c7cfa08d9a3b8e96a27d7888-300x300.png)
Statement
... A statement is a substitution instance of a statement form if it can be obtained by substituting statements into the statement variables of the form. The statement "Roses are red or violets are blue" is a substitution instance of the statement form "p or q", because it can be obtained by substitutin ...
... A statement is a substitution instance of a statement form if it can be obtained by substituting statements into the statement variables of the form. The statement "Roses are red or violets are blue" is a substitution instance of the statement form "p or q", because it can be obtained by substitutin ...
page 3 A CONVERSE BARCAN FORMULA IN ARISTOTLE`S
... First then take a universal negative with the terms a and b. Now if a belongs to no b, b will not belong to any a; for if it, b, does belong to some a (say to c), it will not be true that a belongs to no b — for c is one of the bs (An pr. I.2, 25a14–17).6 It is the cryptic second sentence that sketc ...
... First then take a universal negative with the terms a and b. Now if a belongs to no b, b will not belong to any a; for if it, b, does belong to some a (say to c), it will not be true that a belongs to no b — for c is one of the bs (An pr. I.2, 25a14–17).6 It is the cryptic second sentence that sketc ...
Propositional Logic
... For the calculus to be complete, we need a small addition, as shown by the following example. Let the formula (A ∨ A) be given as our knowledge base. To show by the resolution rule that from there we can derive (A ∧ A), we must show that the empty clause can be derived from (A ∨ A) ∧ (¬A ∨ ¬A). With ...
... For the calculus to be complete, we need a small addition, as shown by the following example. Let the formula (A ∨ A) be given as our knowledge base. To show by the resolution rule that from there we can derive (A ∧ A), we must show that the empty clause can be derived from (A ∨ A) ∧ (¬A ∨ ¬A). With ...
NAMING, SAYING, AND STRUCTURE Philosophers
... examples of non-structural truths, his account should rule them as such. I will argue that the account fails to do so. The illusion to the contrary is created by artificially restricting attention to a subset of possible languages. Sider’s characterization of structural truth is developed by conside ...
... examples of non-structural truths, his account should rule them as such. I will argue that the account fails to do so. The illusion to the contrary is created by artificially restricting attention to a subset of possible languages. Sider’s characterization of structural truth is developed by conside ...
