Full version - Villanova Computer Science
... They can be divided into two major classes: Hilbert-style and Gentzen-style. Hilbert-style systems are axiom-based while Gentzen-style systems are rule-based. Gentzen-style systems have a number of advantages, including existence of straightforward proof search algorithms. In this course we will dea ...
... They can be divided into two major classes: Hilbert-style and Gentzen-style. Hilbert-style systems are axiom-based while Gentzen-style systems are rule-based. Gentzen-style systems have a number of advantages, including existence of straightforward proof search algorithms. In this course we will dea ...
(draft)
... 2 Constructive Logic (a.k.a. Intuitionistic) In Constructive Logic one needs to prove a logical formula is true by proving it is true, not by proving the negation is false (proof by contradiction). While the latter might be perfectly acceptable in classical logic, that method cannot be used in the C ...
... 2 Constructive Logic (a.k.a. Intuitionistic) In Constructive Logic one needs to prove a logical formula is true by proving it is true, not by proving the negation is false (proof by contradiction). While the latter might be perfectly acceptable in classical logic, that method cannot be used in the C ...
Sequent calculus - Wikipedia, the free encyclopedia
... In proof theory and mathematical logic, the sequent calculus is a widely known deduction system for first-order logic (and propositional logic as a special case of it). The system is also known under the name LK, distinguishing it from various other systems of similar fashion that have been created ...
... In proof theory and mathematical logic, the sequent calculus is a widely known deduction system for first-order logic (and propositional logic as a special case of it). The system is also known under the name LK, distinguishing it from various other systems of similar fashion that have been created ...
Practice Problem Set 1
... • Mutual discussion and discussion with the instructor/TA is strongly encouraged. 1. [From HW1, Autumn 2011] Use the proof system of first order logic studied in class to prove each of the following sequents. You must indicate which proof rule you are applying at each step. (a) ∀x∀y. ((P (x) ∨ Q(y) ...
... • Mutual discussion and discussion with the instructor/TA is strongly encouraged. 1. [From HW1, Autumn 2011] Use the proof system of first order logic studied in class to prove each of the following sequents. You must indicate which proof rule you are applying at each step. (a) ∀x∀y. ((P (x) ∨ Q(y) ...
First-order logic;
... Representation: Understand the relationships between different representations of the same information or idea. I ...
... Representation: Understand the relationships between different representations of the same information or idea. I ...
Welcome to CS 245
... What about the “Computation” part? What is the role of computation in our study of logic? Computers are really good at syntactic manipulation. We can use computers, therefore, to implement proof-checkers and other tools to assist us in proving theorems (catching mistakes, proving some simple result ...
... What about the “Computation” part? What is the role of computation in our study of logic? Computers are really good at syntactic manipulation. We can use computers, therefore, to implement proof-checkers and other tools to assist us in proving theorems (catching mistakes, proving some simple result ...
Pre-Greek math
... Motives for re-conceptualization of mathematics in 19th century • Attempts to establish a consistent foundation for mathematics – one that is free from paradoxes “In both situations [Greeks vs. 16th century and 16th vs. 19th century], crises had developed which threatened the security of mathematic ...
... Motives for re-conceptualization of mathematics in 19th century • Attempts to establish a consistent foundation for mathematics – one that is free from paradoxes “In both situations [Greeks vs. 16th century and 16th vs. 19th century], crises had developed which threatened the security of mathematic ...
Probabilistic Propositional Logic
... (which is really only O(2n) –no worse than the (deterministic) prop logic • The real problem is assessing probabilities. – You could need as many as 2n numbers (if all variables are dependent on all other variables); or just n numbers if each variable is independent of all other variables. Generally ...
... (which is really only O(2n) –no worse than the (deterministic) prop logic • The real problem is assessing probabilities. – You could need as many as 2n numbers (if all variables are dependent on all other variables); or just n numbers if each variable is independent of all other variables. Generally ...
CIS160 Mathematical Foundations of Computer Science Some Notes
... 10 CHAPTER 1. MATHEMATICAL REASONING, PROOF PRINCIPLES AND LOGIC ...
... 10 CHAPTER 1. MATHEMATICAL REASONING, PROOF PRINCIPLES AND LOGIC ...
Completeness Theorem for Continuous Functions and Product
... such that (A, ∈) is a model of KP. The smallest example of an admissible set is the set of hereditarily finite sets HF which corresponds to classical computability theory. Another example of an admissible set, important in this paper, is the set HC of hereditarily countable sets. To emphasize the ana ...
... such that (A, ∈) is a model of KP. The smallest example of an admissible set is the set of hereditarily finite sets HF which corresponds to classical computability theory. Another example of an admissible set, important in this paper, is the set HC of hereditarily countable sets. To emphasize the ana ...
Lecture Notes in Computer Science
... Several recent extensions of definite Horn clause programming, especially those with a proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only o ...
... Several recent extensions of definite Horn clause programming, especially those with a proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only o ...
Notes Predicate Logic II
... The theorem states that every valid sequent can be proven, and every sequent that can be proven is valid. This theorem was proven by Kurt Gödel in 1929 in his doctoral dissertation. A description of his proof, as well as the proofs of the following theorems, is beyond the scope of this chapter. The ...
... The theorem states that every valid sequent can be proven, and every sequent that can be proven is valid. This theorem was proven by Kurt Gödel in 1929 in his doctoral dissertation. A description of his proof, as well as the proofs of the following theorems, is beyond the scope of this chapter. The ...
Handout 14
... provable is a tautology. Thus, the formal system of propositional logic is not only sound (i.e. generates only valid formulas) but also generates all of them. Theorem 5.2 (completeness of propositional logic). Let T be a set of formulas and A a formula. Then T (A ...
... provable is a tautology. Thus, the formal system of propositional logic is not only sound (i.e. generates only valid formulas) but also generates all of them. Theorem 5.2 (completeness of propositional logic). Let T be a set of formulas and A a formula. Then T (A ...