AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... Kanger points out that by imposing certain formal requirements on the accessibility relation, like reflexivity, symmetry, transitivity, etc., one can make the operator satisfy corresponding well-known axioms of modal logic. In this way, the introduction of accessibility relations made it possible to ...
... Kanger points out that by imposing certain formal requirements on the accessibility relation, like reflexivity, symmetry, transitivity, etc., one can make the operator satisfy corresponding well-known axioms of modal logic. In this way, the introduction of accessibility relations made it possible to ...
Power Point Presentation
... One problem of calibration is that it does not consider information from the judgment so that nothing can be said about the error rate. If a meteorologist predicts rain at a probability of 55% for each day, his judgment is well calibrated if it rains at 55% of the days in the long run. ...
... One problem of calibration is that it does not consider information from the judgment so that nothing can be said about the error rate. If a meteorologist predicts rain at a probability of 55% for each day, his judgment is well calibrated if it rains at 55% of the days in the long run. ...
Decidable models of small theories
... The set AP T of all almost prime models of a theory T is preordered by the relation of elementary embeddability. The preorder induces a partial order on the factor-set AP T / ∼, where A ∼ B ⇔ (A B & B A), in the natural way. Note that (AP T / ∼, ) has a unique least element—the prime model of ...
... The set AP T of all almost prime models of a theory T is preordered by the relation of elementary embeddability. The preorder induces a partial order on the factor-set AP T / ∼, where A ∼ B ⇔ (A B & B A), in the natural way. Note that (AP T / ∼, ) has a unique least element—the prime model of ...
The Logic of Provability
... Similarly, t < t0 is ∆ for any terms t, t0 . Note further that the class of ∆ formulas is closed under negation and conjunction: the negation of a ∆ formula is always a ∆ formula and the conjunction of two ∆ formulas is itself a ∆ formula. With these in hand, it follows easily that the ∆ formulas ar ...
... Similarly, t < t0 is ∆ for any terms t, t0 . Note further that the class of ∆ formulas is closed under negation and conjunction: the negation of a ∆ formula is always a ∆ formula and the conjunction of two ∆ formulas is itself a ∆ formula. With these in hand, it follows easily that the ∆ formulas ar ...
Lesson 1
... This apple is an agaric. ---------------------------------------------------------------------Hence This apple has a strong toxic effect. The argument is valid. But the conclusion is evidently not true (false). Hence, at least one premise is false (obviously the second). Circumstances according to ...
... This apple is an agaric. ---------------------------------------------------------------------Hence This apple has a strong toxic effect. The argument is valid. But the conclusion is evidently not true (false). Hence, at least one premise is false (obviously the second). Circumstances according to ...
Second-order Logic
... variable assignment s, and a formula ϕ: M, s |= ϕ holds iff what ϕ expresses when its constant symbols, function symbols, and predicate symbols are interpreted as M says, and its free variables are interpreted as s says, is true. The interpretation of the identity predicate = is built into the defin ...
... variable assignment s, and a formula ϕ: M, s |= ϕ holds iff what ϕ expresses when its constant symbols, function symbols, and predicate symbols are interpreted as M says, and its free variables are interpreted as s says, is true. The interpretation of the identity predicate = is built into the defin ...
Strict Predicativity 3
... possibility that might be explored is to admit transfinite levels, as was done in the study of predicativity given the natural numbers. There would be no difficulty in working with an ordering < of the natural numbers that is quite simple, say Δ0, to represent the ordinal levels. Then we would index ...
... possibility that might be explored is to admit transfinite levels, as was done in the study of predicativity given the natural numbers. There would be no difficulty in working with an ordering < of the natural numbers that is quite simple, say Δ0, to represent the ordinal levels. Then we would index ...
slides
... Idea of a (propositional) logic program A logic program is given by a list of (propositional) formulas F1 , F2 , . . . , Fn . A goal is given by another formula G . The task of the system is to determine whether F1 , . . . , Fn |= G . If so, the system returns ‘yes’. Otherwise the system returns ‘n ...
... Idea of a (propositional) logic program A logic program is given by a list of (propositional) formulas F1 , F2 , . . . , Fn . A goal is given by another formula G . The task of the system is to determine whether F1 , . . . , Fn |= G . If so, the system returns ‘yes’. Otherwise the system returns ‘n ...
The Surprise Examination Paradox and the Second Incompleteness
... We give a new proof for the second incompleteness theorem, based on Chaitin’s incompleteness theorem and an argument that resembles the surprise examination paradox, (also known as the unexpected hanging paradox). The surprise examination paradox: the teacher announces in class: “next week you are g ...
... We give a new proof for the second incompleteness theorem, based on Chaitin’s incompleteness theorem and an argument that resembles the surprise examination paradox, (also known as the unexpected hanging paradox). The surprise examination paradox: the teacher announces in class: “next week you are g ...
minimalism and truth
... “Bachelors are unmarried men”, but grasping the concept man does not consist inter alia in grasping that platitude. At least normally, that platitude may help introduce us to the concept bachelor, but not to the concept man: there is simply no question that one can know what a man is without knowing ...
... “Bachelors are unmarried men”, but grasping the concept man does not consist inter alia in grasping that platitude. At least normally, that platitude may help introduce us to the concept bachelor, but not to the concept man: there is simply no question that one can know what a man is without knowing ...
On the futility of criticizing the neoclassical maximization hypothesis
... advantage to the critics over those who argue in its favor. Recall that we distinguish between those statements which are verifiable (i.e. can be proven true) and those which are refutable (i.e. can be proven false) on purely logical grounds. As we know, (strictly) universal statements – those of th ...
... advantage to the critics over those who argue in its favor. Recall that we distinguish between those statements which are verifiable (i.e. can be proven true) and those which are refutable (i.e. can be proven false) on purely logical grounds. As we know, (strictly) universal statements – those of th ...
DISCRETE MATHEMATICAL STRUCTURES - Atria | e
... Subset: We say that A is a subset of set B, or A is contained in B, and we represent it ―A ⊆ B‖, if all elements of A are in B, e.g., if A = {a, b, c} and B = {a, b, c, d, e} then A ⊆ B. Proper subset: A is a proper subset of B, represented ―A ⊂ B‖, if A ⊆ B but A = B, i.e., there is some element in ...
... Subset: We say that A is a subset of set B, or A is contained in B, and we represent it ―A ⊆ B‖, if all elements of A are in B, e.g., if A = {a, b, c} and B = {a, b, c, d, e} then A ⊆ B. Proper subset: A is a proper subset of B, represented ―A ⊂ B‖, if A ⊆ B but A = B, i.e., there is some element in ...
THE ABUNDANCE OF THE FUTURE A Paraconsistent Approach to
... “utility” of this logical approach in the worst case. In order to defeat criticisms of the second kind one should give a possible application, or at least a natural interpretation of this logic. Abundance has at least some intuitive grounding in our linguistic use: most of the times, when we say “ ...
... “utility” of this logical approach in the worst case. In order to defeat criticisms of the second kind one should give a possible application, or at least a natural interpretation of this logic. Abundance has at least some intuitive grounding in our linguistic use: most of the times, when we say “ ...
Basic Set Theory
... Some new notation is required and we must introduce an important piece of mathematical culture. If we say “A if and only if B” then we mean that either A and B are both true or they are both false in any given circumstance. For example: “an integer x is even if and only if it is a multiple of 2”. Th ...
... Some new notation is required and we must introduce an important piece of mathematical culture. If we say “A if and only if B” then we mean that either A and B are both true or they are both false in any given circumstance. For example: “an integer x is even if and only if it is a multiple of 2”. Th ...
p - Erwin Sitompul
... Argument and Proof The truth value of some statements about the world is obvious and easy to assign. The truth of other statements may not be so obvious, but it may still follow (be derived) from known facts about the world. To show the truth value (validity) of such a statement following from ...
... Argument and Proof The truth value of some statements about the world is obvious and easy to assign. The truth of other statements may not be so obvious, but it may still follow (be derived) from known facts about the world. To show the truth value (validity) of such a statement following from ...
A simple proof of Parsons` theorem
... In fact, for x = tj (c, d1 , . . . , dj−1 ) take y = dj and use the fact that ¬ϕ is a universal formula and, therefore, downward absolute between M and M∗ . We have restricted the statement of the theorem to single variables u, x and y in order to make the proof more readable. It is clear, however ...
... In fact, for x = tj (c, d1 , . . . , dj−1 ) take y = dj and use the fact that ¬ϕ is a universal formula and, therefore, downward absolute between M and M∗ . We have restricted the statement of the theorem to single variables u, x and y in order to make the proof more readable. It is clear, however ...
1 QUINE`S INTERPRETATION PROBLEM AND THE EARLY
... predicate language L with predicate symbols and individual constants, but no function symbols. In addition to Boolean connectives, quantifiers and the identity symbol = (considered as a logical symbol), the language L also contains the modal operator M for logical necessity. We assume that L comes w ...
... predicate language L with predicate symbols and individual constants, but no function symbols. In addition to Boolean connectives, quantifiers and the identity symbol = (considered as a logical symbol), the language L also contains the modal operator M for logical necessity. We assume that L comes w ...
First-Order Predicate Logic (2) - Department of Computer Science
... over S. Then G follows from X (is a semantic consequence of X) if the following implication holds for every S-structure F : If F |= E for all E ∈ X, then F |= G. This is denoted by X |= G Observations • For any first-order sentence G: ∅ |= G if, and only if, G is a tautology. Since ‘being a tautolog ...
... over S. Then G follows from X (is a semantic consequence of X) if the following implication holds for every S-structure F : If F |= E for all E ∈ X, then F |= G. This is denoted by X |= G Observations • For any first-order sentence G: ∅ |= G if, and only if, G is a tautology. Since ‘being a tautolog ...