Meta-Ethics and the Problem of Creeping
... about shortly. Second, had Ayer taken his own lesson to heart, he could not possibly have written about the meaning of ethical statements as he in fact did, since by his own remarks on truth there is no obvious content to the insistence that moral statements cannot be true or false. (He has provided ...
... about shortly. Second, had Ayer taken his own lesson to heart, he could not possibly have written about the meaning of ethical statements as he in fact did, since by his own remarks on truth there is no obvious content to the insistence that moral statements cannot be true or false. (He has provided ...
Sample pages 2 PDF
... of values a basic variable can take ranges over an infinite collection. 2.3.1.1 Negation Consider negation. We would like to draw up a table which precisely describes the value of ¬P for any possible value of proposition P . The following table should satisfy our needs: P ...
... of values a basic variable can take ranges over an infinite collection. 2.3.1.1 Negation Consider negation. We would like to draw up a table which precisely describes the value of ¬P for any possible value of proposition P . The following table should satisfy our needs: P ...
Set Theory II
... Last time we discussed the Axioms of Extension, Specification, Unordered Pairs, and Unions. Some more aioms of set theory Powers For each set there exists a collection of sets that contains among its elements all the subsets of the given set. (Combined with the Axiom of Specification, it follows tha ...
... Last time we discussed the Axioms of Extension, Specification, Unordered Pairs, and Unions. Some more aioms of set theory Powers For each set there exists a collection of sets that contains among its elements all the subsets of the given set. (Combined with the Axiom of Specification, it follows tha ...
Ambiguity, generality, and
... generality is defined as a relation among lexical items of a language; yet it is obscured in both (4) and (6), where it is defined, not as a relation, but as a property. Moreover, the relata of the relation are words, and not simply expressions of any sort. Thus, generality is not defined between th ...
... generality is defined as a relation among lexical items of a language; yet it is obscured in both (4) and (6), where it is defined, not as a relation, but as a property. Moreover, the relata of the relation are words, and not simply expressions of any sort. Thus, generality is not defined between th ...
On Perfect Introspection with Quantifying-in
... knowledge about themselves. In other words, while such agents may have incomplete beliefs about the world, they always have complete knowledge about their own beliefs by way of their ability to introspect. Thus it seems that the beliefs of a perfectly introspective agent should be completely determi ...
... knowledge about themselves. In other words, while such agents may have incomplete beliefs about the world, they always have complete knowledge about their own beliefs by way of their ability to introspect. Thus it seems that the beliefs of a perfectly introspective agent should be completely determi ...
Bilattices In Logic Programming
... The domain of the intended model for L(B) will be the Herbrand universe (of closed terms), familiar from Prolog semantics (see [17]). We greatly broaden the notion of formula, however. To this end we assume we have formal symbols, ∧, ∨, ⊗, ⊕ and ¬, corresponding to the various operations on the bila ...
... The domain of the intended model for L(B) will be the Herbrand universe (of closed terms), familiar from Prolog semantics (see [17]). We greatly broaden the notion of formula, however. To this end we assume we have formal symbols, ∧, ∨, ⊗, ⊕ and ¬, corresponding to the various operations on the bila ...
logic for computer science - Institute for Computing and Information
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
Review - UT Computer Science
... The wff w2 is not valid. It is also unsatisfiable since it is false in all interpretations, which follows from the fact that w2 is valid. Finally, let w3 be the wff: x (P(x, x)) The wff w3 is not valid but it is satisfiable. Suppose that the universe is the integers and P is the predicate LessTha ...
... The wff w2 is not valid. It is also unsatisfiable since it is false in all interpretations, which follows from the fact that w2 is valid. Finally, let w3 be the wff: x (P(x, x)) The wff w3 is not valid but it is satisfiable. Suppose that the universe is the integers and P is the predicate LessTha ...
Propositional and predicate logic - Computing Science
... x P(x) is read “For all x’es, P (x) is true”. E.g., for all TRU COMP students, they are smart. x P(x) is read “there exists an x such that P(x) is true”. E.g., there is a TRU COMP student who is not smart. ...
... x P(x) is read “For all x’es, P (x) is true”. E.g., for all TRU COMP students, they are smart. x P(x) is read “there exists an x such that P(x) is true”. E.g., there is a TRU COMP student who is not smart. ...
A short article for the Encyclopedia of Artificial Intelligence: Second
... over functions and predicates. Leibniz’s principle of equality, for example, states that two objects are to be taken as equal if they share the same properties; that is, a = b can be defined as ∀P [P (a) ≡ P (b)]. Of course, first-order logic is very strong and it is possible to encode such a statem ...
... over functions and predicates. Leibniz’s principle of equality, for example, states that two objects are to be taken as equal if they share the same properties; that is, a = b can be defined as ∀P [P (a) ≡ P (b)]. Of course, first-order logic is very strong and it is possible to encode such a statem ...
possible-worlds semantics for modal notions conceived as predicates
... We have several qualms about this approach. As above, we do not see any good reason to treat truth and necessity (and the other predicates) differently on the syntactical level. Furthermore the theory of necessity and other notions would rest on truth-theoretic foundations which are threatened by th ...
... We have several qualms about this approach. As above, we do not see any good reason to treat truth and necessity (and the other predicates) differently on the syntactical level. Furthermore the theory of necessity and other notions would rest on truth-theoretic foundations which are threatened by th ...
2.3 Weakest Preconditions
... just a Boolean combination of atomic formulae over the program variables. – In particular, quantifiers are not allowed: if we want to check that ∀1 ≤ i < N.something holds, then we must write an explicit do loop over i for it. • Guarded commands separate logic which is expressed with guards and just ...
... just a Boolean combination of atomic formulae over the program variables. – In particular, quantifiers are not allowed: if we want to check that ∀1 ≤ i < N.something holds, then we must write an explicit do loop over i for it. • Guarded commands separate logic which is expressed with guards and just ...
Intuitionistic Type Theory
... the interpretation of propositions as truth values and propositional functions (of one or several variables) as truth functions. The laws of the classical propositional logic are then clearly valid, and so are the quantifier laws, as long as quantification is restricted to finite domains. However, i ...
... the interpretation of propositions as truth values and propositional functions (of one or several variables) as truth functions. The laws of the classical propositional logic are then clearly valid, and so are the quantifier laws, as long as quantification is restricted to finite domains. However, i ...
Constructive Set Theory and Brouwerian Principles1
... the axiom of continuous choice (CC), the fan theorem (FT), and monotone bar induction (BIM ). The objective is to determine whether these principles increase the proof-theoretic strength of CZF. More precisely, the research is concerned with the question of whether any new Π20 statements of arithmet ...
... the axiom of continuous choice (CC), the fan theorem (FT), and monotone bar induction (BIM ). The objective is to determine whether these principles increase the proof-theoretic strength of CZF. More precisely, the research is concerned with the question of whether any new Π20 statements of arithmet ...