Dissolving the Scandal of Propositional Logic?
... the scandal succeeds? No. For I do not agree with Valk that [1**] is a proper formalization of [1]-[2]. For [1**] is much too strong. Is someone who asserts [1]-[2] really committed to the claim that for all formulas P, Q and R it is the case that if P ∧ Q → R is a tautology, P → R or Q → R is a tau ...
... the scandal succeeds? No. For I do not agree with Valk that [1**] is a proper formalization of [1]-[2]. For [1**] is much too strong. Is someone who asserts [1]-[2] really committed to the claim that for all formulas P, Q and R it is the case that if P ∧ Q → R is a tautology, P → R or Q → R is a tau ...
Coordinate-free logic - Utrecht University Repository
... different than saying that there are ‘out there’ a less-than relation and a greaterthan relation. In my view, people who think there are really two such relations are misled by language. It seems hard to deny that 4’s being less than 6 is the very same fact as 6’s being greater than 4. In English an ...
... different than saying that there are ‘out there’ a less-than relation and a greaterthan relation. In my view, people who think there are really two such relations are misled by language. It seems hard to deny that 4’s being less than 6 is the very same fact as 6’s being greater than 4. In English an ...
Formal Reasoning - Institute for Computing and Information Sciences
... The sentence ‘if a and b, then a’ is true, whatever you substitute for a and b. So, we’d like to be able to say: the sentence ‘a ∧ b → a’ is true2 . But we can’t, because we haven’t formally defined what that means yet. As of yet, ‘a ∧ b → a’ is only one of the words of our formal language. Which is ...
... The sentence ‘if a and b, then a’ is true, whatever you substitute for a and b. So, we’d like to be able to say: the sentence ‘a ∧ b → a’ is true2 . But we can’t, because we haven’t formally defined what that means yet. As of yet, ‘a ∧ b → a’ is only one of the words of our formal language. Which is ...
Discrete Mathematics
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
Determination of the Differentiably Simple Rings with a
... case in what we shall show in ?6 is an equivalentform. simplerings is as menThe above resulton the non-simpledifferentiably theorem. One aspect of that tioned analogous to the Wedderburn-Artin rings in that theoremis played here analogyis that the role of the division by simplerings,and in the assoc ...
... case in what we shall show in ?6 is an equivalentform. simplerings is as menThe above resulton the non-simpledifferentiably theorem. One aspect of that tioned analogous to the Wedderburn-Artin rings in that theoremis played here analogyis that the role of the division by simplerings,and in the assoc ...
Points, lines and diamonds: a two-sorted modal logic for projective
... language MLG 2 is two-sorted as well: we will distinguish point formulas and line formulas. The language then will have two diamonds with respectively the incidence relation and its converse as accessibility relation. These diamonds thus turn respectively line formulas into point formulas, and vice ...
... language MLG 2 is two-sorted as well: we will distinguish point formulas and line formulas. The language then will have two diamonds with respectively the incidence relation and its converse as accessibility relation. These diamonds thus turn respectively line formulas into point formulas, and vice ...
