PPTX
... Learning goals: in-class • By the end of this module, you should be able to • Determine whether or not a propositional logic proof is valid, and explain why it is valid or invalid. • Explore the consequences of a set of propositional logic statements by application of equivalence and inference rule ...
... Learning goals: in-class • By the end of this module, you should be able to • Determine whether or not a propositional logic proof is valid, and explain why it is valid or invalid. • Explore the consequences of a set of propositional logic statements by application of equivalence and inference rule ...
ch1_Logic_and_proofs
... are definitions: Two triangles are congruent if their vertices can be paired so that the corresponding sides are equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
... are definitions: Two triangles are congruent if their vertices can be paired so that the corresponding sides are equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
One Problem with the Material Conditional
... But wait! This affirms that G (the antecedent) is True and A (the consequent) is false But using our example sentence, this entails that “God exists” is True! So, counter-intuitively, the person who denies that an All-powerful being exists if God exists is logically committed to the assertion that G ...
... But wait! This affirms that G (the antecedent) is True and A (the consequent) is false But using our example sentence, this entails that “God exists” is True! So, counter-intuitively, the person who denies that an All-powerful being exists if God exists is logically committed to the assertion that G ...
Logic of Natural Language Semantics: Presuppositions and
... d. CIs are logically and compositionally independent of what is ‘said (in the favored sense)’, i.e. independent of the at-issue entailments. In this talk, I mainly present Potts (2005) that shows a range of different empirical phenomena such as expressive expressions, appositive nominals (ANs) or ap ...
... d. CIs are logically and compositionally independent of what is ‘said (in the favored sense)’, i.e. independent of the at-issue entailments. In this talk, I mainly present Potts (2005) that shows a range of different empirical phenomena such as expressive expressions, appositive nominals (ANs) or ap ...
notes
... that we can think of ¬φ as corresponding to a function τ → 0. We have seen functions that accept a type and do not return a value before: continuations have that behavior. If φ corresponds to τ , a reasonable interpretation of ¬φ is as a continuation expecting a τ . Negation corresponds to turning o ...
... that we can think of ¬φ as corresponding to a function τ → 0. We have seen functions that accept a type and do not return a value before: continuations have that behavior. If φ corresponds to τ , a reasonable interpretation of ¬φ is as a continuation expecting a τ . Negation corresponds to turning o ...
Dissolving the Scandal of Propositional Logic?
... dependence between two statements. It was introduced to capture the notion of implication or logical consequence in natural language. So having to rely on an adjunctive interpretation of material implication is not part of the solution. It is part of the problem. Or more apt: it is the problem. The ...
... dependence between two statements. It was introduced to capture the notion of implication or logical consequence in natural language. So having to rely on an adjunctive interpretation of material implication is not part of the solution. It is part of the problem. Or more apt: it is the problem. The ...
characterization of prime numbers by
... a denumerable set of propositional variables {p, q, r, ...} say, and the two connectives: ¬ (negation) and ⊃ (implication). Finally, we define Lukasiewicz’s n-valued logic Ln to be the set of all tautologies of the matrix ML n , i.e. the set of all formulas α such that v(α) = n−1 for each valuation ...
... a denumerable set of propositional variables {p, q, r, ...} say, and the two connectives: ¬ (negation) and ⊃ (implication). Finally, we define Lukasiewicz’s n-valued logic Ln to be the set of all tautologies of the matrix ML n , i.e. the set of all formulas α such that v(α) = n−1 for each valuation ...
Monadic Predicate Logic is Decidable
... Proof of Part 2 Making use of Part 1, associate with S a quantifier-free formula S’ which is satisfiable iff S is. As follows: Inductively associate a quantifier-free H’ with each subformula H of S, as follows: • If H is atomic: H’=H (no change!) • If H is a truth functional compound: H’=H • If H=E ...
... Proof of Part 2 Making use of Part 1, associate with S a quantifier-free formula S’ which is satisfiable iff S is. As follows: Inductively associate a quantifier-free H’ with each subformula H of S, as follows: • If H is atomic: H’=H (no change!) • If H is a truth functional compound: H’=H • If H=E ...
Predicate Logic
... • Propositional logic is the simplest way of attempting representing knowledge in logic using symbols. – Symbols represent facts: P, Q, etc.. – These are joined by logical connectives (and, or, implication) e.g., P Q; Q R – Given some statements in the logic we can deduce new facts (e.g., from a ...
... • Propositional logic is the simplest way of attempting representing knowledge in logic using symbols. – Symbols represent facts: P, Q, etc.. – These are joined by logical connectives (and, or, implication) e.g., P Q; Q R – Given some statements in the logic we can deduce new facts (e.g., from a ...
Logic Agents and Propositional Logic
... If search returns failure (after some number of tries) we ...
... If search returns failure (after some number of tries) we ...
Document
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
propositions and connectives propositions and connectives
... connectives – each has one or more meanings in natural language – need for precise, formal language ...
... connectives – each has one or more meanings in natural language – need for precise, formal language ...
T - RTU
... in First-Order Logic The semantics of first-order logic provide a basis for a formal theory of logical inference. The ability to infer new correct expressions from a set of true assertions is very important feature of first-order logic. These new expressions are correct in that they are consistent w ...
... in First-Order Logic The semantics of first-order logic provide a basis for a formal theory of logical inference. The ability to infer new correct expressions from a set of true assertions is very important feature of first-order logic. These new expressions are correct in that they are consistent w ...
First order theories
... A: Adding axioms to the theory may make it harder to decide or even undecidable. ...
... A: Adding axioms to the theory may make it harder to decide or even undecidable. ...