Propositional/First
... • A valid sentence is true in all worlds under all interpretations • If an implication sentence can be shown to be valid, then—given its premise—its consequent can be derived • Different logics make different commitments about what the world is made of and what kind of beliefs we can have regarding ...
... • A valid sentence is true in all worlds under all interpretations • If an implication sentence can be shown to be valid, then—given its premise—its consequent can be derived • Different logics make different commitments about what the world is made of and what kind of beliefs we can have regarding ...
Lecture 9. Model theory. Consistency, independence, completeness
... of the sentences in ∆ hold in the model.) And if the answer is NO, usually the easiest way to show it is by deriving a contradiction, i.e. by showing that ∆ ├ ⊥. See homework problems 5-8. 2.4. Independence. The notion of independence is less crucial than some of the other notions we have studied; i ...
... of the sentences in ∆ hold in the model.) And if the answer is NO, usually the easiest way to show it is by deriving a contradiction, i.e. by showing that ∆ ├ ⊥. See homework problems 5-8. 2.4. Independence. The notion of independence is less crucial than some of the other notions we have studied; i ...
Scoring Rubric for Assignment 1
... all presented accurately; Theory is relevant, accurately described and all relevant components are included; relationship between research and theory is clearly articulated and accurate. 8– 10 pts Conclusion is clearly stated and connections to the research and position are clear and relevant. The u ...
... all presented accurately; Theory is relevant, accurately described and all relevant components are included; relationship between research and theory is clearly articulated and accurate. 8– 10 pts Conclusion is clearly stated and connections to the research and position are clear and relevant. The u ...
The semantics of predicate logic
... The interpretations for quantifiers are more complex, but clearly inspired by, the interpretations for ∧ and ∨. As an aside, the dependence of interpretations on environments can also be expressed using λ-notation: ...
... The interpretations for quantifiers are more complex, but clearly inspired by, the interpretations for ∧ and ∨. As an aside, the dependence of interpretations on environments can also be expressed using λ-notation: ...
Natural deduction
... “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 argument to persuade you skeptics. (If you’re not a skeptic, just trust ...
... “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 argument to persuade you skeptics. (If you’re not a skeptic, just trust ...
A HIGHER-ORDER FINE-GRAINED LOGIC FOR INTENSIONAL
... of the set of functions from SA to SB . We take a boolean prelattice to be a set B with a preorder (a relation that is transitive, reflexive, but not antisymmetic) v, two nullary operations T and F , one unary operation 0 (written postfix), and four binary operations u, t, ⇒, ⇔, subject to the follo ...
... of the set of functions from SA to SB . We take a boolean prelattice to be a set B with a preorder (a relation that is transitive, reflexive, but not antisymmetic) v, two nullary operations T and F , one unary operation 0 (written postfix), and four binary operations u, t, ⇒, ⇔, subject to the follo ...
handout
... Intuitionistic logic is the basis of constructive mathematics. Constructive mathematics takes a much more conservative view of truth than classical mathematics. It is concerned less with truth than with provability. Two of its main proponents were Kronecker and Brouwer. These views generated great c ...
... Intuitionistic logic is the basis of constructive mathematics. Constructive mathematics takes a much more conservative view of truth than classical mathematics. It is concerned less with truth than with provability. Two of its main proponents were Kronecker and Brouwer. These views generated great c ...
