A Proof Theory for Generic Judgments: An extended abstract
... need to discover invariants. Another more intensional approach, however, involves introducing a new, generic variable, say, c : γ, that has not been introduced before in the proof, and to prove the formula B[c/x] instead. In natural deduction and sequent calculus proofs, such new variables are calle ...
... need to discover invariants. Another more intensional approach, however, involves introducing a new, generic variable, say, c : γ, that has not been introduced before in the proof, and to prove the formula B[c/x] instead. In natural deduction and sequent calculus proofs, such new variables are calle ...
Logic and Resolution - Institute for Computing and Information
... a given formula F the truth value true, then w is called a model for F . By repeated applications of the rules listed in table 2.1, it is possible to express the truth value of an arbitrary formula in terms of the truth values of the atoms the formula is composed of. In a formula containing n differ ...
... a given formula F the truth value true, then w is called a model for F . By repeated applications of the rules listed in table 2.1, it is possible to express the truth value of an arbitrary formula in terms of the truth values of the atoms the formula is composed of. In a formula containing n differ ...
Knowledge Representation and Reasoning
... propositions — called premisses — which match certain patterns, we can deduce that some further proposition is true — this is called the conclusion. Thus we saw that from two propositions with the forms α → β and α we can deduce β. The inference from P → Q and P to Q is of this form. An inference ru ...
... propositions — called premisses — which match certain patterns, we can deduce that some further proposition is true — this is called the conclusion. Thus we saw that from two propositions with the forms α → β and α we can deduce β. The inference from P → Q and P to Q is of this form. An inference ru ...
Chapter 1 Logic
... Since logical equivalence is defined in terms of a statement being a tautology, a truth table can be used to check if (prove that) two statements are logically equivalent. Soon we will have other methods to do this as well. ...
... Since logical equivalence is defined in terms of a statement being a tautology, a truth table can be used to check if (prove that) two statements are logically equivalent. Soon we will have other methods to do this as well. ...
Justification logic with approximate conditional probabilities
... {ϕ → CP≤r+ n1 (α, β) | n ≥ 1−r , n ∈ N} infer ϕ → CP≈r (α, β). 5. From P≤0 α infer ¬α, for α ∈ FmlJ . Axiom 3, putting > instead of β, says that the probability of each formula being satisfied in some set of worlds is at least 0, and we can easily infer (using ¬α instead of α) that the upper bound i ...
... {ϕ → CP≤r+ n1 (α, β) | n ≥ 1−r , n ∈ N} infer ϕ → CP≈r (α, β). 5. From P≤0 α infer ¬α, for α ∈ FmlJ . Axiom 3, putting > instead of β, says that the probability of each formula being satisfied in some set of worlds is at least 0, and we can easily infer (using ¬α instead of α) that the upper bound i ...
Coordinate-free logic - Utrecht University Repository
... It should be noted that, in this paper, for the mathematical results only elementary finitistic reasoning will be used. If we would use for our reasoning an existing foundation like set theory, then we would continue to be stuck with the old foundation. 1 Parts of Section 2 and Section 3 have been p ...
... It should be noted that, in this paper, for the mathematical results only elementary finitistic reasoning will be used. If we would use for our reasoning an existing foundation like set theory, then we would continue to be stuck with the old foundation. 1 Parts of Section 2 and Section 3 have been p ...
1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN
... At roughly the same time, in a series of papers (see in particular [1930, 1930a]), Tarski studied logical consequence in an abstract axiomatic way, where purely syntactical aspects of the matter are prominent. In his syntactical studies, Tarski’s basic notion was not a consequence relation between a ...
... At roughly the same time, in a series of papers (see in particular [1930, 1930a]), Tarski studied logical consequence in an abstract axiomatic way, where purely syntactical aspects of the matter are prominent. In his syntactical studies, Tarski’s basic notion was not a consequence relation between a ...
