Interpreting Lattice-Valued Set Theory in Fuzzy Set Theory
... This paper presents a comparison of two axiomatic set theories over two non-classical logics. In particular, it suggests an interpretation of lattice-valued set theory as defined in [16] by S. Titani in fuzzy set theory as defined in [11] by authors of this paper. There are many different conception ...
... This paper presents a comparison of two axiomatic set theories over two non-classical logics. In particular, it suggests an interpretation of lattice-valued set theory as defined in [16] by S. Titani in fuzzy set theory as defined in [11] by authors of this paper. There are many different conception ...
Saturation of Sets of General Clauses
... 2. In the proof, it does not really matter with which negative literal an inference is performed ⇒ choose a negative literal don’t-care-nondeterministically ⇒ selection ...
... 2. In the proof, it does not really matter with which negative literal an inference is performed ⇒ choose a negative literal don’t-care-nondeterministically ⇒ selection ...
Phil 2302 Intro to Logic
... major premise, and an unconditional minor premise leading to an unconditional conclusion. 1. A conditional major premise. 2. An unconditional minor premise. 3. An unconditional conclusion. Rather than having three terms as categorical syllogisms do, a hypothetical syllogism has only two terms. Inste ...
... major premise, and an unconditional minor premise leading to an unconditional conclusion. 1. A conditional major premise. 2. An unconditional minor premise. 3. An unconditional conclusion. Rather than having three terms as categorical syllogisms do, a hypothetical syllogism has only two terms. Inste ...
Nonmonotonic Reasoning - Computer Science Department
... in 1928. More recently, there has been much activity in formalizing the logics of ”I know ...”, and ”I believe... P”. But it is only since 1980 or so, under the influence of John McCarthy, that non-monotonic reasoning as such has been systematically formalized. McCarthy, building on the efforts of ear ...
... in 1928. More recently, there has been much activity in formalizing the logics of ”I know ...”, and ”I believe... P”. But it is only since 1980 or so, under the influence of John McCarthy, that non-monotonic reasoning as such has been systematically formalized. McCarthy, building on the efforts of ear ...
Day00a-Induction-proofs - Rose
... • How do we actually construct a proof by strong induction? To show that p(n) is true for all n n0 : – Step 0: Believe in the "magic." • You will show that it's not really magic at all. But you have to believe. • If, when you are in the middle of an induction proof, you begin to doubt whether the ...
... • How do we actually construct a proof by strong induction? To show that p(n) is true for all n n0 : – Step 0: Believe in the "magic." • You will show that it's not really magic at all. But you have to believe. • If, when you are in the middle of an induction proof, you begin to doubt whether the ...
On Elkan`s theorems: Clarifying their meaning
... omitted from the first version of Elkan’s theorem. As to the rest of the assumptions, both t~A ∧ B! ⫽ min$t~A!, t~B!% and t~¬A! ⫽ 1 ⫺ t~A! are quite reasonable and, in fact, are often used in applications of fuzzy logic. Let us now concentrate on the last assumption, that is, on t~A! ⫽ t~B! if A and ...
... omitted from the first version of Elkan’s theorem. As to the rest of the assumptions, both t~A ∧ B! ⫽ min$t~A!, t~B!% and t~¬A! ⫽ 1 ⫺ t~A! are quite reasonable and, in fact, are often used in applications of fuzzy logic. Let us now concentrate on the last assumption, that is, on t~A! ⫽ t~B! if A and ...
Properties of Independently Axiomatizable Bimodal Logics
... Let EL denote the lattice of extensions of a modal logic. We have defined an operation − ⊗ − : (EK)2 → EK2 . ⊗ is a -homomorphism in both arguments. There are certain easy properties of this map which are noteworthy. Fixing the second argument we can study the map − ⊗ M : EK → EK2 . This is a -h ...
... Let EL denote the lattice of extensions of a modal logic. We have defined an operation − ⊗ − : (EK)2 → EK2 . ⊗ is a -homomorphism in both arguments. There are certain easy properties of this map which are noteworthy. Fixing the second argument we can study the map − ⊗ M : EK → EK2 . This is a -h ...
An Introduction to Prolog Programming
... A Prolog program corresponds to a set of formulas, all of which are assumed to be true. This restricts the range of possible interpretations of the predicate and function symbols appearing in these formulas. The formulas in the translated program may be thought of as the premises in a proof. If Prol ...
... A Prolog program corresponds to a set of formulas, all of which are assumed to be true. This restricts the range of possible interpretations of the predicate and function symbols appearing in these formulas. The formulas in the translated program may be thought of as the premises in a proof. If Prol ...
Document
... • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) is true • In other words, show th ...
... • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) is true • In other words, show th ...
First-Order Logic, Second-Order Logic, and Completeness
... a conceptual analysis using a deductive system? Logic, after all, is about inference, and so are deductive systems.8 All these issues are important, and good arguments have been put forward on both sides. The above paragraph certainly does not faithfully represent the complexity of the actual debate ...
... a conceptual analysis using a deductive system? Logic, after all, is about inference, and so are deductive systems.8 All these issues are important, and good arguments have been put forward on both sides. The above paragraph certainly does not faithfully represent the complexity of the actual debate ...
Exam 2 Sample
... 3. (10 pts) (a) How many different 5-card poker hands are there? (b) How many different 5-card poker hands make a "full house" (3 cards have one value, and the other two cards have another value -- for example, 3 kings and 2 tens)? For possible partial credit, explain your reasoning. (c) How many di ...
... 3. (10 pts) (a) How many different 5-card poker hands are there? (b) How many different 5-card poker hands make a "full house" (3 cards have one value, and the other two cards have another value -- for example, 3 kings and 2 tens)? For possible partial credit, explain your reasoning. (c) How many di ...
Rewriting in the partial algebra of typed terms modulo AC
... happens in each dimension of the vector is dissociated from the other components, petri nets possess subtle parallelism facilities. On the other hand the expressiveness over control flow is quiet weak (e.g. it is impossible to encode a stack). The fundamental result over petri nets is the problem of ...
... happens in each dimension of the vector is dissociated from the other components, petri nets possess subtle parallelism facilities. On the other hand the expressiveness over control flow is quiet weak (e.g. it is impossible to encode a stack). The fundamental result over petri nets is the problem of ...
