On Equivalent Transformations of Infinitary Formulas under the
... Main Theorem. For any set H of formulas, (a) if a formula F is provable in the basic system then H ∪ {F } has the same stable models as H; (b) if F is equivalent to G in the basic system then H ∪ {F } and H ∪ {G} have the same stable models. Lemma 1. For any formula F and interpretation I, if I does ...
... Main Theorem. For any set H of formulas, (a) if a formula F is provable in the basic system then H ∪ {F } has the same stable models as H; (b) if F is equivalent to G in the basic system then H ∪ {F } and H ∪ {G} have the same stable models. Lemma 1. For any formula F and interpretation I, if I does ...
Chapter 4. Logical Notions This chapter introduces various logical
... m to represent a logical form. It is important, however, not to identify a formula with the logical form it represents. p and q, for example, should be taken to represent the same form, as should (pZq) and (rZs). In general, two formulas will represent the same form when they have the same (concrete ...
... m to represent a logical form. It is important, however, not to identify a formula with the logical form it represents. p and q, for example, should be taken to represent the same form, as should (pZq) and (rZs). In general, two formulas will represent the same form when they have the same (concrete ...
A Resolution-Based Proof Method for Temporal Logics of
... This paper presents two logics, called KLn and BLn respectively, and gives resolutionbased proof methods for both. The logic KLn is a temporal logic of knowledge. That is, in addition to the usual connectives of linear discrete temporal logic [4], KLn contains an indexed set of unary modal connectiv ...
... This paper presents two logics, called KLn and BLn respectively, and gives resolutionbased proof methods for both. The logic KLn is a temporal logic of knowledge. That is, in addition to the usual connectives of linear discrete temporal logic [4], KLn contains an indexed set of unary modal connectiv ...
Document
... A proposition is a declarative sentence that is either TRUE or FALSE (not both). Examples: ...
... A proposition is a declarative sentence that is either TRUE or FALSE (not both). Examples: ...
A Brief Introduction to the Intuitionistic Propositional Calculus
... Problem 1 Prove that α ⇒ (β ⇒ γ) `I (α ∧ β) ⇒ γ. Problem 2 Show that α ⇒ β 6`I ¬α ∨ β by demonstrating that there exists a Kripke model K = (W, ≤, |=) and a world w ∈ W such that w |= α ⇒ β, but w 6|= ¬α ∨ β. Problem 3 Show that world w1 in the simple Kripke model in Section 4 does not satisfy Peirc ...
... Problem 1 Prove that α ⇒ (β ⇒ γ) `I (α ∧ β) ⇒ γ. Problem 2 Show that α ⇒ β 6`I ¬α ∨ β by demonstrating that there exists a Kripke model K = (W, ≤, |=) and a world w ∈ W such that w |= α ⇒ β, but w 6|= ¬α ∨ β. Problem 3 Show that world w1 in the simple Kripke model in Section 4 does not satisfy Peirc ...
Chapter 2 Notes
... Example 5: Edmund and Roberto took a 7 day (168 hours), 90 mile canoe trip down the Allagash River. If they paddled at an average rate of 2.5 miles per hour, how many hours did they not spend paddling? Write an equation to find the answer. ...
... Example 5: Edmund and Roberto took a 7 day (168 hours), 90 mile canoe trip down the Allagash River. If they paddled at an average rate of 2.5 miles per hour, how many hours did they not spend paddling? Write an equation to find the answer. ...
Global linear convergence of an augmented Lagrangian algorithm
... it is clear from the structure of the AL in (2.2) that a large r gives priority to the restoration of the equality constraint, leaving aside the minimization of the Lagrangian (whose role is to provide optimality). In comparison with an interior point method, which faces the combinatorial aspect of ...
... it is clear from the structure of the AL in (2.2) that a large r gives priority to the restoration of the equality constraint, leaving aside the minimization of the Lagrangian (whose role is to provide optimality). In comparison with an interior point method, which faces the combinatorial aspect of ...
How to Prove Properties by Induction on Formulas
... A few comments may be helpful. First, the propositional logic meaning of implies is crucial for making this proof work in case (ii) for each of the connectives. As soon as the hypothesis is false, the truth of the implication “comes for free.” Second, in the induction, I’ve tried to make it clear wh ...
... A few comments may be helpful. First, the propositional logic meaning of implies is crucial for making this proof work in case (ii) for each of the connectives. As soon as the hypothesis is false, the truth of the implication “comes for free.” Second, in the induction, I’ve tried to make it clear wh ...
An Unsolvable Problem of Elementary Number Theory Alonzo
... 1. Introduction. There is a class of problems of elementary number theory which can be stated in the form that i t is required to find an effectively calculable function f of n positive integers, such that f (x,, x,, . . . ,x,) = 2 is a necessary and sufficient condition for the truth of a certain p ...
... 1. Introduction. There is a class of problems of elementary number theory which can be stated in the form that i t is required to find an effectively calculable function f of n positive integers, such that f (x,, x,, . . . ,x,) = 2 is a necessary and sufficient condition for the truth of a certain p ...