Sets
... Boolean data type If statement Impact of negations Implementation of quantifiers Discrete Mathematical Structures: Theory and Applications ...
... Boolean data type If statement Impact of negations Implementation of quantifiers Discrete Mathematical Structures: Theory and Applications ...
Ordered Groups: A Case Study In Reverse Mathematics 1 Introduction
... vague term that is best explained by an example. Complete separable metric spaces are essentially countable because, although the spaces may be uncountable, they can be understood in terms of a countable basis. Simpson (1985) gives the following list of areas which can be analyzed by reverse mathema ...
... vague term that is best explained by an example. Complete separable metric spaces are essentially countable because, although the spaces may be uncountable, they can be understood in terms of a countable basis. Simpson (1985) gives the following list of areas which can be analyzed by reverse mathema ...
CARLOS AUGUSTO DI PRISCO The notion of infinite appears in
... The construction of the model M [g] and the proof that it has the desired properties is quite elaborate. Certain elements of the model M are used as “names” for elements of M [g]. Which set is the object named by a name τ depends on the generic g, and given g, the model M [g] is the collection of se ...
... The construction of the model M [g] and the proof that it has the desired properties is quite elaborate. Certain elements of the model M are used as “names” for elements of M [g]. Which set is the object named by a name τ depends on the generic g, and given g, the model M [g] is the collection of se ...
Clausal Logic and Logic Programming in Algebraic Domains*
... and sets of models as Scott-compact saturated sets. The main result yields a compactness theorem for any clausal logic over a coherent algebraic domain. We prove the usual compactness theorem in classical logic as a corollary. Next we show that the resolution rule, appropriately generalized to claus ...
... and sets of models as Scott-compact saturated sets. The main result yields a compactness theorem for any clausal logic over a coherent algebraic domain. We prove the usual compactness theorem in classical logic as a corollary. Next we show that the resolution rule, appropriately generalized to claus ...
CS3234 Logic and Formal Systems
... 5 B This is not a correct proof because Line 5 is inside a box, but uses Lines 1 and 2, which are outside the box. ...
... 5 B This is not a correct proof because Line 5 is inside a box, but uses Lines 1 and 2, which are outside the box. ...
Logic and Automata - Cheriton School of Computer Science
... In this case, we do not need to convert an NFA to a DFA. We can check acceptance with depth-first search, by seeing if there is a path in the automaton from the initial state q0 to a state of F . This can be done in time linear in the size of the automaton. Similarly, if we want to know if there are ...
... In this case, we do not need to convert an NFA to a DFA. We can check acceptance with depth-first search, by seeing if there is a path in the automaton from the initial state q0 to a state of F . This can be done in time linear in the size of the automaton. Similarly, if we want to know if there are ...
Frege`s Other Program
... work here were developed in connection with a reconstruction of Frege’s own approach to logical metatheory, his so-called New Science—see Antonelli and May [1].) This requires a second-order language that allows explicit quantification over predicates, relations, and so on, as well as ordinary first ...
... work here were developed in connection with a reconstruction of Frege’s own approach to logical metatheory, his so-called New Science—see Antonelli and May [1].) This requires a second-order language that allows explicit quantification over predicates, relations, and so on, as well as ordinary first ...
SORT LOGIC AND FOUNDATIONS OF MATHEMATICS 1
... In computer science it is commonplace to regard a database as a manysorted structure. Each column (attribute) of the database has its own range of values, be it a salary figure, gender, department, last name, zip code, or whatever. In fact, it would seem very unnatural to lump all these together int ...
... In computer science it is commonplace to regard a database as a manysorted structure. Each column (attribute) of the database has its own range of values, be it a salary figure, gender, department, last name, zip code, or whatever. In fact, it would seem very unnatural to lump all these together int ...
Peano`s Arithmetic
... is a number (a ɛ N), then a × 1 = a, which is a number. Therefore, the number 1 works as b from the thesis (as described by “1 ɛ [bɛ]Ts”). The next line is the induction step; it is assumed that if b is a number and takes the place of the b from the thesis (“b ɛ [ɛ]Ts”), then a×b is a number. Then i ...
... is a number (a ɛ N), then a × 1 = a, which is a number. Therefore, the number 1 works as b from the thesis (as described by “1 ɛ [bɛ]Ts”). The next line is the induction step; it is assumed that if b is a number and takes the place of the b from the thesis (“b ɛ [ɛ]Ts”), then a×b is a number. Then i ...
A constructive approach to nonstandard analysis*
... us here. As for Brouwer intuitionism [B] there is a first attempt by Vesley [31]. Moerdijk and Reyes [20] use topos theory to develop calculus with different kinds of infinitesimals. The logic used in the formal theories of their approach is intuitionistic, but the necessary properties of their mode ...
... us here. As for Brouwer intuitionism [B] there is a first attempt by Vesley [31]. Moerdijk and Reyes [20] use topos theory to develop calculus with different kinds of infinitesimals. The logic used in the formal theories of their approach is intuitionistic, but the necessary properties of their mode ...
Second-order Logic
... first-order logic, and so it is in general more complicated to capture its validities. In fact, we’ll show that second-order logic is not only undecidable, but its validities are not even computably enumerable. This means there can be no sound and complete proof system for second-order logic (althou ...
... first-order logic, and so it is in general more complicated to capture its validities. In fact, we’ll show that second-order logic is not only undecidable, but its validities are not even computably enumerable. This means there can be no sound and complete proof system for second-order logic (althou ...
PPT
... Indirect proofs refer to proof by contrapositive or proof by contradiction which we introduce next . A contrapositive proof or proof by contrapositive for conditional proposition P Q one makes use of the tautology (P Q) ( Q P). Since P Q and Q P are logically equivalent we first g ...
... Indirect proofs refer to proof by contrapositive or proof by contradiction which we introduce next . A contrapositive proof or proof by contrapositive for conditional proposition P Q one makes use of the tautology (P Q) ( Q P). Since P Q and Q P are logically equivalent we first g ...
A Revised Concept of Safety for General Answer Set Programs
... What if we go beyond the syntax of disjunctive programs? Adding negation in the heads of program rules will not require a change in the definition of safety. But for more far reaching language extensions, such as allowing rules with nested expressions, or perhaps even arbitrary first-order formulas, ...
... What if we go beyond the syntax of disjunctive programs? Adding negation in the heads of program rules will not require a change in the definition of safety. But for more far reaching language extensions, such as allowing rules with nested expressions, or perhaps even arbitrary first-order formulas, ...
Computing Default Extensions by Reductions on OR
... the authors state a modal reduction theorem to the effect that a formula O Rϕ is logically equivalent to a disjunction Oϕ1 ∨ · · · ∨ Oϕn , where each ϕk is a propositional formula. Because each such disjunct Oϕ k has a unique model, it is possible, within the logic itself, to break down a formula O ...
... the authors state a modal reduction theorem to the effect that a formula O Rϕ is logically equivalent to a disjunction Oϕ1 ∨ · · · ∨ Oϕn , where each ϕk is a propositional formula. Because each such disjunct Oϕ k has a unique model, it is possible, within the logic itself, to break down a formula O ...