Countability
... two natural numbers. Surprisingly, the two sets have the same cardinality! To see this, let us introduce a slightly different way of comparing the cardinality of two sets. If there is a one-to-one function f : A → B, then the cardinality of A is less than or equal to that of B. Now to show that the ...
... two natural numbers. Surprisingly, the two sets have the same cardinality! To see this, let us introduce a slightly different way of comparing the cardinality of two sets. If there is a one-to-one function f : A → B, then the cardinality of A is less than or equal to that of B. Now to show that the ...
Week 1: Logic Lecture 1, 8/21 (Sections 1.1 and 1.3)
... false led to a contradiction, the claim must be true. Proving equivalence. In math, we have many ways of saying the same thing. We can express the statement ...
... false led to a contradiction, the claim must be true. Proving equivalence. In math, we have many ways of saying the same thing. We can express the statement ...
Rewriting in the partial algebra of typed terms modulo AC
... [12,9] (given two states, is it possible to find a path of transitions leading from the first to the second one). However the properties decidable over Petri nets are far more simple than the one decidable for pushdown systems (for instance checking whether the set of states reachable by two Petri n ...
... [12,9] (given two states, is it possible to find a path of transitions leading from the first to the second one). However the properties decidable over Petri nets are far more simple than the one decidable for pushdown systems (for instance checking whether the set of states reachable by two Petri n ...
Recall... Venn Diagrams Disjunctive normal form Disjunctive normal
... A set of Boolean operators is said to be functionally complete if it can be used to express all possible Boolean expressions. ...
... A set of Boolean operators is said to be functionally complete if it can be used to express all possible Boolean expressions. ...
Basic Set Theory
... The opening and closing curly braces denote a set, 2n specifies the members of the set, the colon says “such that” or “where” and everything following the colon are conditions that explain or refine the membership. All correct mathematics can be spoken in English. The set definition above is spoken ...
... The opening and closing curly braces denote a set, 2n specifies the members of the set, the colon says “such that” or “where” and everything following the colon are conditions that explain or refine the membership. All correct mathematics can be spoken in English. The set definition above is spoken ...
Clausal Logic and Logic Programming in Algebraic Domains*
... provide a model for non-monotonic reasoning in AI, as exemplified by Reiter’s default logic [Rei80]. We used the Smyth powerdomain, in its model-theoretic incarnation as a domain of compact saturated sets, as a setting for a semantic version of default reasoning called power default reasoning [ZR97a ...
... provide a model for non-monotonic reasoning in AI, as exemplified by Reiter’s default logic [Rei80]. We used the Smyth powerdomain, in its model-theoretic incarnation as a domain of compact saturated sets, as a setting for a semantic version of default reasoning called power default reasoning [ZR97a ...
