Slides
... A generic framework for reducing decidable logics to propositional logic (beyond NP). ...
... A generic framework for reducing decidable logics to propositional logic (beyond NP). ...
Induction
... Let P(x) be a predicate statement, whose universe of discourse is the natural numbers. Suppose the following are true statements. 1) Base Case: P(1) : the statement is true for n = 1 2) Induction Hypothesis: P(n) implies P(n+1): the statement being true for n implies the statement is true for n +1 I ...
... Let P(x) be a predicate statement, whose universe of discourse is the natural numbers. Suppose the following are true statements. 1) Base Case: P(1) : the statement is true for n = 1 2) Induction Hypothesis: P(n) implies P(n+1): the statement being true for n implies the statement is true for n +1 I ...
Natural deduction
... Conditional proof and validity • At this point you might wonder. . . “yeah, I could see how the other rules were valid from the truth-tables, but this one is pretty weird! what’s the deal?” – in other words, you may not be persuaded that conditional proof preserves validity • So here is a little arg ...
... Conditional proof and validity • At this point you might wonder. . . “yeah, I could see how the other rules were valid from the truth-tables, but this one is pretty weird! what’s the deal?” – in other words, you may not be persuaded that conditional proof preserves validity • So here is a little arg ...
Predicate logic
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
03_Artificial_Intelligence-PredicateLogic
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
Predicate logic - Teaching-WIKI
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
Predicate logic
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
... • Intuitionistic first-order logic uses intuitionistic rather than classical propositional calculus; for example, ¬¬φ need not be equivalent to φ • Infinitary logic allows infinitely long sentences; for example, one may allow a conjunction or disjunction of infinitely many formulas, or quantificatio ...
PDF
... remains is the case when A has the form D. We do induction on the number n of ’s in A. The case when n = 0 means that A is a wff of PLc , and has already been proved. Now suppose A has n + 1 ’s. Then D has n ’s, and so by induction, ` D[B/p] ↔ D[C/p], and therefore ` D[B/p] ↔ D[C/p] by 2. This ...
... remains is the case when A has the form D. We do induction on the number n of ’s in A. The case when n = 0 means that A is a wff of PLc , and has already been proved. Now suppose A has n + 1 ’s. Then D has n ’s, and so by induction, ` D[B/p] ↔ D[C/p], and therefore ` D[B/p] ↔ D[C/p] by 2. This ...
Curry`s Paradox. An Argument for Trivialism
... A being a dialetheia should lead dialetheists to reject the classical equivalence between (A→ B) and (¬A ∨ B). This equivalence holds in classical logic because the truth of (¬A ∨ B) guarantees that truth is preserved from A to B for the reason that dialetheiae are excluded. Of course, nothing preve ...
... A being a dialetheia should lead dialetheists to reject the classical equivalence between (A→ B) and (¬A ∨ B). This equivalence holds in classical logic because the truth of (¬A ∨ B) guarantees that truth is preserved from A to B for the reason that dialetheiae are excluded. Of course, nothing preve ...
Theories.Axioms,Rules of Inference
... concerns a given theory in a given logic. That theory is a set of axioms. The logic has rules of inference that allow us to generate other theorems from those axioms. (Axioms are theorems.) When we start ACL2, it has lots of functions already defined and it correspondingly has axioms for those funct ...
... concerns a given theory in a given logic. That theory is a set of axioms. The logic has rules of inference that allow us to generate other theorems from those axioms. (Axioms are theorems.) When we start ACL2, it has lots of functions already defined and it correspondingly has axioms for those funct ...
Cocktail
... Integrate the extended automated theorem prover to deal with equational reasoning. Constructing a new, more elaborate programming language. Allow for derivation and post-verification of programs within a single tool. Integrate other approaches and tools within the same framework. ...
... Integrate the extended automated theorem prover to deal with equational reasoning. Constructing a new, more elaborate programming language. Allow for derivation and post-verification of programs within a single tool. Integrate other approaches and tools within the same framework. ...