A Computing Procedure for Quantification Theory
... We i n t r o d u c e t h e following a b b r e v i a t i v e c o n v e n t i o n s : a s t a n d s for f~. f s t a n d s for f2. pq s t a n d s for p ( q ) if p is a f u n c t i o n s y m b o l a n d q is a t e r m . ~ ( p l , p2, "'" , pn) s t a n d s for "-~p(pl, " " , pn), where p is a p r e d i ...
... We i n t r o d u c e t h e following a b b r e v i a t i v e c o n v e n t i o n s : a s t a n d s for f~. f s t a n d s for f2. pq s t a n d s for p ( q ) if p is a f u n c t i o n s y m b o l a n d q is a t e r m . ~ ( p l , p2, "'" , pn) s t a n d s for "-~p(pl, " " , pn), where p is a p r e d i ...
work-pavan1
... biconditional conjunction <-> as p<->q and is read as “p only if q” and “p if q”. "p if and only if q" f. Tautology: A compound proposition, which is true in every case. E.g.: pV q p V p g. Contradiction: This is the opposite of tautology, which is false in every case. E.g.: p^q p^p Logical impl ...
... biconditional conjunction <-> as p<->q and is read as “p only if q” and “p if q”. "p if and only if q" f. Tautology: A compound proposition, which is true in every case. E.g.: pV q p V p g. Contradiction: This is the opposite of tautology, which is false in every case. E.g.: p^q p^p Logical impl ...
Lecture 3
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
2/TRUTH-FUNCTIONS
... Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement connectives: and, or, if...then, if and only if. When written in symbols they may be called logical operators. s7. Truth Values [TV]: statement either affirms/denies. Hence either ...
... Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement connectives: and, or, if...then, if and only if. When written in symbols they may be called logical operators. s7. Truth Values [TV]: statement either affirms/denies. Hence either ...
.pdf
... the dummy of (∀x)P . We abbreviate (∀x)P by (x)P (as does Church [2]). An occurrence of individual variable x is bound in formula P iff the occurrence is within a subformula of P of the form (x)Q ; otherwise, the occurrence of x is free in P . Precedence conventions allow the elimination of some pare ...
... the dummy of (∀x)P . We abbreviate (∀x)P by (x)P (as does Church [2]). An occurrence of individual variable x is bound in formula P iff the occurrence is within a subformula of P of the form (x)Q ; otherwise, the occurrence of x is free in P . Precedence conventions allow the elimination of some pare ...
1 Deductive Reasoning and Logical Connectives
... If a variable is used to stand for an object, we may be interested in talking about the properties of the object. For example, to express that a number is prime, we can use x to represent the number. To express the statement “x is prime”, so far we have been using some Boolean variable such as p. Ho ...
... If a variable is used to stand for an object, we may be interested in talking about the properties of the object. For example, to express that a number is prime, we can use x to represent the number. To express the statement “x is prime”, so far we have been using some Boolean variable such as p. Ho ...
Lecture Notes 3
... Entered ^ Drove(john,car(john),house(john)) – OK? No – the truth functional connectives connect sentences, not predicates Entered(john,car(john)) ^ Drove(john,house(john)) – This is OK ...
... Entered ^ Drove(john,car(john),house(john)) – OK? No – the truth functional connectives connect sentences, not predicates Entered(john,car(john)) ^ Drove(john,house(john)) – This is OK ...
IS IT EASY TO LEARN THE LOGIC
... For a logic student, the problem that appears at first sight in the text 1 is the lack of syntax clarity to be symbolized in propositional logic (PL); in other words, it is difficult for him to construct the following formal structure which corresponds to that text: If q then r, and if s then t; the ...
... For a logic student, the problem that appears at first sight in the text 1 is the lack of syntax clarity to be symbolized in propositional logic (PL); in other words, it is difficult for him to construct the following formal structure which corresponds to that text: If q then r, and if s then t; the ...
Completeness of Propositional Logic Truth Assignments and Truth
... Truth Assignments and Truth Tables Let us define a truth assignment for a first-order language to be any function h from the set of all atomic sentences of that language into the set {TRUE, FALSE}. That is, for each atomic sentence A of the language, h gives us a truth value, written h(A), either TR ...
... Truth Assignments and Truth Tables Let us define a truth assignment for a first-order language to be any function h from the set of all atomic sentences of that language into the set {TRUE, FALSE}. That is, for each atomic sentence A of the language, h gives us a truth value, written h(A), either TR ...
CS 2742 (Logic in Computer Science) Lecture 6
... This is another way to describe “proof by contrapositive”. Similarly we can write the proof by cases, by contradiction, by transitivity and so on. They can be derived from the original logic identities. For example, modus ponens becomes ((p → q) ∧ p) → q. ...
... This is another way to describe “proof by contrapositive”. Similarly we can write the proof by cases, by contradiction, by transitivity and so on. They can be derived from the original logic identities. For example, modus ponens becomes ((p → q) ∧ p) → q. ...
term 1 - Teaching-WIKI
... • In propositional logic the smallest atoms represent whole propositions (propositions are atomic) – Propositional logic does not capture the internal structure of the propositions – It is not possible to work with units smaller than a proposition ...
... • In propositional logic the smallest atoms represent whole propositions (propositions are atomic) – Propositional logic does not capture the internal structure of the propositions – It is not possible to work with units smaller than a proposition ...
slides
... F1 , F2 , . . . , Fn , notation F1 , . . . , Fn |= G , iff, for all interpretations I, if I |= F1 and . . . and I |= Fn then I |= G . Don’t get confused! The symbol |= is used in two different ways: I |= F F1 , . . . , Fn |= G In the first the left-hand-side is an interpretation, in the second it is ...
... F1 , F2 , . . . , Fn , notation F1 , . . . , Fn |= G , iff, for all interpretations I, if I |= F1 and . . . and I |= Fn then I |= G . Don’t get confused! The symbol |= is used in two different ways: I |= F F1 , . . . , Fn |= G In the first the left-hand-side is an interpretation, in the second it is ...
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 ...