Implication - Abstractmath.org
... Pascal does not have variables or expressions of type proposition. It does have Boolean variables, which have TRUE and FALSE as their only possible values. An expression such as ` X
... Pascal does not have variables or expressions of type proposition. It does have Boolean variables, which have TRUE and FALSE as their only possible values. An expression such as ` X
Lecture Slides
... Suppose the statement has the form: ∀x ∈ D, P(x) → Q(x) This is a special case of the previous formula The textbook calls this (and only this) a direct proof. The proof looks like this: Proof: o Consider an unspecified element k of D. o Assume that P(k) is true. o Use this and properties of ...
... Suppose the statement has the form: ∀x ∈ D, P(x) → Q(x) This is a special case of the previous formula The textbook calls this (and only this) a direct proof. The proof looks like this: Proof: o Consider an unspecified element k of D. o Assume that P(k) is true. o Use this and properties of ...
The Premiss-Based Approach to Logical Aggregation Franz Dietrich & Philippe Mongin
... in public places (b), if smoking is harmful, then it should be banned in public places (a ! b), and so on. Assume further that the collective judgments are obtained by aggregating the individual judgments - this is the judgment aggregation problem. A natural approach consists in singling out those p ...
... in public places (b), if smoking is harmful, then it should be banned in public places (a ! b), and so on. Assume further that the collective judgments are obtained by aggregating the individual judgments - this is the judgment aggregation problem. A natural approach consists in singling out those p ...
An Institution-Independent Generalization of Tarski`s Elementary
... logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulae by means of classical first-order connectives and quantifiers. These include the unconditional equational, positive, (Π ∪ Σ)0n , and full first-order logics, as well as less conventional logics, used ...
... logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulae by means of classical first-order connectives and quantifiers. These include the unconditional equational, positive, (Π ∪ Σ)0n , and full first-order logics, as well as less conventional logics, used ...
Logic and Proof
... Every animal is mortal. Therefore every man is mortal. Aristotle observed that the correctness of this inference has nothing to do with the truth or falsity of the individual statements, but, rather, the general pattern: Every A is B. Every B is C. Therefore every A is C. We can substitute various p ...
... Every animal is mortal. Therefore every man is mortal. Aristotle observed that the correctness of this inference has nothing to do with the truth or falsity of the individual statements, but, rather, the general pattern: Every A is B. Every B is C. Therefore every A is C. We can substitute various p ...
The Journal of Functional and Logic Programming The MIT Press
... as terms in the Herbrand universe. Actually, all the CLP(X ) systems in which X is not FT or an extension of it1 still retain the possibility of building uninterpreted terms, and so are at least CLP(FT , X ) systems. Furthermore, many systems support several constraint domains, as mentioned above. T ...
... as terms in the Herbrand universe. Actually, all the CLP(X ) systems in which X is not FT or an extension of it1 still retain the possibility of building uninterpreted terms, and so are at least CLP(FT , X ) systems. Furthermore, many systems support several constraint domains, as mentioned above. T ...
Introduction to Mathematical Logic lecture notes
... we will be able to deduce (or “prove”) formulae from other formulae. Indeed, in real-life Mathematics, a proof is merely a sequence of assertions (alas, in an informal natural ...
... we will be able to deduce (or “prove”) formulae from other formulae. Indeed, in real-life Mathematics, a proof is merely a sequence of assertions (alas, in an informal natural ...
PPT - UBC Department of CPSC Undergraduates
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
Dedukti
... quantifiers ∀ and ∃. For instance, it is not possible to define, in predicate logic, a unary function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicat ...
... quantifiers ∀ and ∃. For instance, it is not possible to define, in predicate logic, a unary function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicat ...
Conjecture
... If a set of graphs has a decidable MS2 satisfiability problem, it has bounded tree-width. Conjecture (Seese 1991) : If a set of graphs has a decidable MS satisfiability problem, it is the image of a set of trees under an MS transduction, equivalently, has bounded cliquewidth. Theorem (B.C., S. Oum 2 ...
... If a set of graphs has a decidable MS2 satisfiability problem, it has bounded tree-width. Conjecture (Seese 1991) : If a set of graphs has a decidable MS satisfiability problem, it is the image of a set of trees under an MS transduction, equivalently, has bounded cliquewidth. Theorem (B.C., S. Oum 2 ...
full text (.pdf)
... a representation theorem was proved showing that every termset algebra is isomorphic to a set-theoretic termset algebra. These models include the standard models in which set expressions are interpreted as sets of ground terms, as well as nonstandard models in which set expressions are interpreted a ...
... a representation theorem was proved showing that every termset algebra is isomorphic to a set-theoretic termset algebra. These models include the standard models in which set expressions are interpreted as sets of ground terms, as well as nonstandard models in which set expressions are interpreted a ...