Judgment and consequence relations
... “whenever”. By saying “whenever” we effectively quantify over valuations. We take (1) to say that whatever valuation makes all members of ∆ true must also make ϕ true. If ∆ ∅ this is equivalent to saying that ϕ is a tautology. As already indicated, we may also think of logical consequence as prese ...
... “whenever”. By saying “whenever” we effectively quantify over valuations. We take (1) to say that whatever valuation makes all members of ∆ true must also make ϕ true. If ∆ ∅ this is equivalent to saying that ϕ is a tautology. As already indicated, we may also think of logical consequence as prese ...
22c:145 Artificial Intelligence
... given a set Γ = {α1 , . . . , αm } of sentences and a sentence ϕ, may reply “yes”, “no”, or runs forever. If I replies positively to input (Γ, ϕ), we say that Γ derives ϕ in I , a and write Γ /I ϕ Intuitively, I should be such that it replies “yes” on input (Γ, ϕ) only if ϕ is in fact entailed by Γ. ...
... given a set Γ = {α1 , . . . , αm } of sentences and a sentence ϕ, may reply “yes”, “no”, or runs forever. If I replies positively to input (Γ, ϕ), we say that Γ derives ϕ in I , a and write Γ /I ϕ Intuitively, I should be such that it replies “yes” on input (Γ, ϕ) only if ϕ is in fact entailed by Γ. ...
x - Stanford University
... As with predicates, functions can take in any number of arguments, but each function has a fixed arity. Functions evaluate to objects, not propositions. There is no syntactic way to distinguish functions and predicates; you'll have to look at how they're used. ...
... As with predicates, functions can take in any number of arguments, but each function has a fixed arity. Functions evaluate to objects, not propositions. There is no syntactic way to distinguish functions and predicates; you'll have to look at how they're used. ...
Proof Theory: From Arithmetic to Set Theory
... • The patterns of reasoning described by Stoic logic are the patterns of interconnection between propositions that are completely independent of what those propositions say. • The first known systematic study of logic which involved quantifiers, components such as “for all” and “some”, was carried o ...
... • The patterns of reasoning described by Stoic logic are the patterns of interconnection between propositions that are completely independent of what those propositions say. • The first known systematic study of logic which involved quantifiers, components such as “for all” and “some”, was carried o ...
Default Logic (Reiter) - Department of Computing
... Remark: integrity constraints Recall the so-called metalevel or epistemic reading of an integrity constraint “if α then β” Informally, this is ‘if α is in the database then β is in the database’. So, if the database content is Cn(D) (some base D, some notion of consequence Cn) then we are saying: i ...
... Remark: integrity constraints Recall the so-called metalevel or epistemic reading of an integrity constraint “if α then β” Informally, this is ‘if α is in the database then β is in the database’. So, if the database content is Cn(D) (some base D, some notion of consequence Cn) then we are saying: i ...
Basic Logic and Fregean Set Theory - MSCS
... of these models, and often lead to more efficient and more natural derivations of the relevant properties. It appears that classical mathematics and logic is just one of several useful extensions of constructive logic. There are of course also variations on constructive logic, if only by just making ...
... of these models, and often lead to more efficient and more natural derivations of the relevant properties. It appears that classical mathematics and logic is just one of several useful extensions of constructive logic. There are of course also variations on constructive logic, if only by just making ...
Chapter 3 - Georgia State University
... atoms. (See Figure 3.1.) It uses a selected atomic formula p(s1 , . . . , sn ) of the goal and a selected program clause of the form p(t1 , . . . , tn ) ← A1 , . . . , Am (where m ≥ 0 and A1 , . . . , Am are atoms) to find a common instance of p(s1 , . . . , sn ) and p(t1 , . . . , tn ). In other wo ...
... atoms. (See Figure 3.1.) It uses a selected atomic formula p(s1 , . . . , sn ) of the goal and a selected program clause of the form p(t1 , . . . , tn ) ← A1 , . . . , Am (where m ≥ 0 and A1 , . . . , Am are atoms) to find a common instance of p(s1 , . . . , sn ) and p(t1 , . . . , tn ). In other wo ...
A brief introduction to Logic and its applications
... Another reason why one could not prove P ∨ ¬P ? When you prove a statement such as A ∨ B you can extract a proof that answers whether A or B holds. If we were able to prove the excluded middle, we could extract an algorithm that, given some proposition tells us whether it is valid or not (Curry-Howa ...
... Another reason why one could not prove P ∨ ¬P ? When you prove a statement such as A ∨ B you can extract a proof that answers whether A or B holds. If we were able to prove the excluded middle, we could extract an algorithm that, given some proposition tells us whether it is valid or not (Curry-Howa ...
CHAPTER 8 Hilbert Proof Systems, Formal Proofs, Deduction
... Hence the Deduction Theorem holds for system H2 . Theorem 3.1 (Deduction Theorem for H2 ) For any subset Γ of the set of formulas F of H2 and for any formulas A, B ∈ F , Γ, A `H2 B if and only if Γ `H2 (A ⇒ B). In particular, A `H2 B if and only if `H2 (A ⇒ B). Obviously, the axioms A1, A2, A3 are t ...
... Hence the Deduction Theorem holds for system H2 . Theorem 3.1 (Deduction Theorem for H2 ) For any subset Γ of the set of formulas F of H2 and for any formulas A, B ∈ F , Γ, A `H2 B if and only if Γ `H2 (A ⇒ B). In particular, A `H2 B if and only if `H2 (A ⇒ B). Obviously, the axioms A1, A2, A3 are t ...
Day00a-Induction-proofs - Rose
... • We must show that k is a product of prime integers – If k is prime, then clearly k is the product of one prime integer – Otherwise k is a composite integer: • i.e., k = j*m, where integers j and m are both greater than one ...
... • We must show that k is a product of prime integers – If k is prime, then clearly k is the product of one prime integer – Otherwise k is a composite integer: • i.e., k = j*m, where integers j and m are both greater than one ...
Syllogistic Logic Sample Quiz Page 1
... I’ll do poorly in logic. I’m sure of this because of the following facts. First, I don’t do LogiCola. Second, I don’t read the book. Third, I spend my time playing Tetris. Assuming that I spend my time playing Tetris and I don’t do LogiCola, then, of course, if I don’t read the book then I’ll do poo ...
... I’ll do poorly in logic. I’m sure of this because of the following facts. First, I don’t do LogiCola. Second, I don’t read the book. Third, I spend my time playing Tetris. Assuming that I spend my time playing Tetris and I don’t do LogiCola, then, of course, if I don’t read the book then I’ll do poo ...
Q - GROU.PS
... Its truth value depends on the value of y, but this value is not specified. We call this type of statement a propositional function or open sentence. Spring 2003 ...
... Its truth value depends on the value of y, but this value is not specified. We call this type of statement a propositional function or open sentence. Spring 2003 ...
![overhead 8/singular sentences [ov]](http://s1.studyres.com/store/data/009258618_1-2a98e952bde8fd34c716ae0716ce6df4-300x300.png)
overhead 8/singular sentences [ov]
... SYMBOLIZING simple singular sentences in predicate logic Singular sentences can be simple or compound. Our example: Los Angeles is sunny. is a simple sentence. To symbolize this sentence: (1) represent the predicate with a PROPOSITIONAL FUNCTION; this is just a technical term for what we get if we p ...
... SYMBOLIZING simple singular sentences in predicate logic Singular sentences can be simple or compound. Our example: Los Angeles is sunny. is a simple sentence. To symbolize this sentence: (1) represent the predicate with a PROPOSITIONAL FUNCTION; this is just a technical term for what we get if we p ...
Introduction to first order logic for knowledge representation
... Is the link that connects the real world with it’s matematical and abstract representation into a mathematical structure. If a certain situation is supposed to be abstractly described by a given structure, then the abstraction connects the elements that participats to the situation, with the compone ...
... Is the link that connects the real world with it’s matematical and abstract representation into a mathematical structure. If a certain situation is supposed to be abstractly described by a given structure, then the abstraction connects the elements that participats to the situation, with the compone ...
19_pl
... “5 is even implies 6 is odd” is True! If P is False, regardless of Q, P Q is True No causality needed: “5 is odd implies the Sun is a star” is True ...
... “5 is even implies 6 is odd” is True! If P is False, regardless of Q, P Q is True No causality needed: “5 is odd implies the Sun is a star” is True ...
Propositional Logic
... instead and still defined its semantics the same way. A ⇒ B “means” A is sufficient but not necessary to make B true Example: § Let A be “has a cold” and B be “drink water” § A ⇒ B can be interpreted as “should drink water” when “has a cold.” § However, you can drink water even when you do not ha ...
... instead and still defined its semantics the same way. A ⇒ B “means” A is sufficient but not necessary to make B true Example: § Let A be “has a cold” and B be “drink water” § A ⇒ B can be interpreted as “should drink water” when “has a cold.” § However, you can drink water even when you do not ha ...
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.