Seventy-five problems for testing automatic
... difficult, or because previous ATP systems have reported difficulties in establishing them, or because they have some interesting connection with other areas of mathematics (such as set theory). The judgements of difficulty are my own, and are based primarily on my years of teaching elementary logic ...
... difficult, or because previous ATP systems have reported difficulties in establishing them, or because they have some interesting connection with other areas of mathematics (such as set theory). The judgements of difficulty are my own, and are based primarily on my years of teaching elementary logic ...
Is the Liar Sentence Both True and False? - NYU Philosophy
... schema is validated as well. We have the naive theory of truth in its entirety; the only cost is dialetheism, for the Liar sentence and its negation will both be consequences of the truth theory. But I do not think this is really much of an improvement over the situation with K3 .6 For the main prob ...
... schema is validated as well. We have the naive theory of truth in its entirety; the only cost is dialetheism, for the Liar sentence and its negation will both be consequences of the truth theory. But I do not think this is really much of an improvement over the situation with K3 .6 For the main prob ...
CHAPTER 1 The main subject of Mathematical Logic is
... For the human reader such representations are less convenient, so we shall stick to the use of bound variables. In the definition of “substitution of expression E 0 for variable x in expression E”, either one requires that no variable free in E 0 becomes bound by a variable-binding operator in E, wh ...
... For the human reader such representations are less convenient, so we shall stick to the use of bound variables. In the definition of “substitution of expression E 0 for variable x in expression E”, either one requires that no variable free in E 0 becomes bound by a variable-binding operator in E, wh ...
MATH 312H–FOUNDATIONS
... say that A is true if there is one t so that A(t) is true, that is ∃t such that A(t) is true, ¬ A to be true requires that there is no t such that A(t) is true, or for all t ¬A(t) holds. A special logical instrument to conlude the truth of a statement is given by Mathematical Induction. We assume th ...
... say that A is true if there is one t so that A(t) is true, that is ∃t such that A(t) is true, ¬ A to be true requires that there is no t such that A(t) is true, or for all t ¬A(t) holds. A special logical instrument to conlude the truth of a statement is given by Mathematical Induction. We assume th ...
A(x)
... The first equivalence is obtained by applying the Deduction Theorem m-times, the second is valid due to the soundness and completeness, the third one is the semantic equivalence. ...
... The first equivalence is obtained by applying the Deduction Theorem m-times, the second is valid due to the soundness and completeness, the third one is the semantic equivalence. ...
A(x)
... The first equivalence is obtained by applying the Deduction Theorem m-times, the second is valid due to the soundness and completeness, the third one is the semantic equivalence. ...
... The first equivalence is obtained by applying the Deduction Theorem m-times, the second is valid due to the soundness and completeness, the third one is the semantic equivalence. ...
Rich Chapter 5 Predicate Logic - Computer Science
... discuss higher order theories in this chapter) as a way of representing knowledge because it permits representations of things that cannot reasonably be represented in prepositional logic. In predicate logic, we can represent real-world facts as statements written as wff's. But a major motivation fo ...
... discuss higher order theories in this chapter) as a way of representing knowledge because it permits representations of things that cannot reasonably be represented in prepositional logic. In predicate logic, we can represent real-world facts as statements written as wff's. But a major motivation fo ...
A Proof Theory for Generic Judgments
... induction can replace the need for infinite premises with finite premises (the base cases and inductive cases) but with the need to discover invariants. Another more intensional approach, however, involves introducing a new variable, say, c : τ , that has not been introduced before in the proof, and ...
... induction can replace the need for infinite premises with finite premises (the base cases and inductive cases) but with the need to discover invariants. Another more intensional approach, however, involves introducing a new variable, say, c : τ , that has not been introduced before in the proof, and ...
Chapter 1
... Mathematicians make explicit our assumptions about mathematical structures. These assumptions are call axioms. From axioms we deduce, logically, other properties and connections. Hence, a requirement for being able to write a mathematical proof is an understanding of logic. While we will not delve i ...
... Mathematicians make explicit our assumptions about mathematical structures. These assumptions are call axioms. From axioms we deduce, logically, other properties and connections. Hence, a requirement for being able to write a mathematical proof is an understanding of logic. While we will not delve i ...
A(x)
... question: having a formula , does the calculus decide ? In other words, is there an algorithm that would answer Yes or No, having as input and answering the question whether is logically valid or no? If there is such an algorithm, then the calculus is decidable. If the calculus is complete, th ...
... question: having a formula , does the calculus decide ? In other words, is there an algorithm that would answer Yes or No, having as input and answering the question whether is logically valid or no? If there is such an algorithm, then the calculus is decidable. If the calculus is complete, th ...
On not strengthening intuitionistic logic
... variable, any expression of the form ~ A, where A is a wff, and any expression of one of the forms (A &B), (A v B), (A D 5 ) , and (A = B), where A and B are wffs. By a turnstile statement (T-statement) we shall understand any expression of the form Aly A2, . . , An V B, where Au A2, . . . , An (n ^ ...
... variable, any expression of the form ~ A, where A is a wff, and any expression of one of the forms (A &B), (A v B), (A D 5 ) , and (A = B), where A and B are wffs. By a turnstile statement (T-statement) we shall understand any expression of the form Aly A2, . . , An V B, where Au A2, . . . , An (n ^ ...
Search problems
... First-Order Logic (abbreviated FOL or FOPC) is expressive enough to concisely represent this kind of situation. ...
... First-Order Logic (abbreviated FOL or FOPC) is expressive enough to concisely represent this kind of situation. ...
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.