Sequent calculus - Wikipedia, the free encyclopedia
... The Sequent calculus LK was introduced by Gerhard Gentzen as a tool for studying natural deduction. It has turned out to be a very useful calculus for constructing logical derivations. The name itself is derived from the German term Logischer Kalkül, meaning "logical calculus." Sequent calculi are t ...
... The Sequent calculus LK was introduced by Gerhard Gentzen as a tool for studying natural deduction. It has turned out to be a very useful calculus for constructing logical derivations. The name itself is derived from the German term Logischer Kalkül, meaning "logical calculus." Sequent calculi are t ...
Chapter 9: Quantified Formulas
... The validity problem of QBF is PSPACE-complete, which means that it is theoretically harder to solve than SAT, which is “only” NP-complete2 . Both of these problems (SAT and and the QBF problem) are frequently presented as the quintessential problems of their respective complexity classes. The known ...
... The validity problem of QBF is PSPACE-complete, which means that it is theoretically harder to solve than SAT, which is “only” NP-complete2 . Both of these problems (SAT and and the QBF problem) are frequently presented as the quintessential problems of their respective complexity classes. The known ...
Lectures on Laws of Supply and Demand, Simple and Compound
... Definition A compound proposition is two or more propositions combined by a logical connective. Example 2 “ If Brian and Angela are not both happy then either Brian is not happy or Angela is not happy”. This is an example of a compound proposition. Logic is not concerned with determining the truth ...
... Definition A compound proposition is two or more propositions combined by a logical connective. Example 2 “ If Brian and Angela are not both happy then either Brian is not happy or Angela is not happy”. This is an example of a compound proposition. Logic is not concerned with determining the truth ...
Multi-Agent Only
... that Bob believes that Tweety flies. But technically things were surprisingly cumbersome! The problem lies in the complexity in what agents consider possible: ...
... that Bob believes that Tweety flies. But technically things were surprisingly cumbersome! The problem lies in the complexity in what agents consider possible: ...
Proof Theory in Type Theory
... The negative translation provides a general way to make constructive sense of some non effective reasoning. However this method has some limitations. It does not work in presence of the axiom of description/choice. In this note, we analyse the interaction of classical logic with generalised inductiv ...
... The negative translation provides a general way to make constructive sense of some non effective reasoning. However this method has some limitations. It does not work in presence of the axiom of description/choice. In this note, we analyse the interaction of classical logic with generalised inductiv ...
Basic Logic - Progetto e
... From Propositional to Predicate Logic Propositional logic is a useful tool for reasoning, but it is limited because it cannot see inside propositions and take advantage of relationships among inner elements. ...
... From Propositional to Predicate Logic Propositional logic is a useful tool for reasoning, but it is limited because it cannot see inside propositions and take advantage of relationships among inner elements. ...
Notes and exercises on First Order Logic
... Variables are placeholders so we must have some means of replacing them with more concrete information. We often need to replace a free variable v by an entire term t, i.e. substitute t for v. In substituting t for v we have to leave untouched the bound occurrences of v since they are in the scope o ...
... Variables are placeholders so we must have some means of replacing them with more concrete information. We often need to replace a free variable v by an entire term t, i.e. substitute t for v. In substituting t for v we have to leave untouched the bound occurrences of v since they are in the scope o ...
UBE 501 DISCRETE MATHEMATICS Fall 2015 QUESTION SET #1
... people, A and B. Determine, if possible, what A and B are if they address you in the way described. If you can not determine what these two people are, can you draw any conclusions? A says “At least one of us is knave” and B says nothing. 4) Use a truth table to verify the first De Morgan law ( p ...
... people, A and B. Determine, if possible, what A and B are if they address you in the way described. If you can not determine what these two people are, can you draw any conclusions? A says “At least one of us is knave” and B says nothing. 4) Use a truth table to verify the first De Morgan law ( p ...
Lecture01 - Mathematics
... Set Theory: Informally we define a set as a collection of objects. The resulting theory of how one can operate on sets is known as naïve set theory. It is naïve because the informal definition leads to subtle paradoxes. A more careful definition of set removes these paradoxes and leaves the conclusi ...
... Set Theory: Informally we define a set as a collection of objects. The resulting theory of how one can operate on sets is known as naïve set theory. It is naïve because the informal definition leads to subtle paradoxes. A more careful definition of set removes these paradoxes and leaves the conclusi ...
A program for the countable choice axiom
... c ) is the set of arbitrary (resp. closed) λc-terms. ¦ is the set of stacks. They are built following these rules : 1. Any variable x, and the constant cc are λc-terms. 2. If t, u are λc-terms and x is a variable, then (t)u and λx t are λc-terms. 3. If π is a stack, the constant kπ is a λc-term (cal ...
... c ) is the set of arbitrary (resp. closed) λc-terms. ¦ is the set of stacks. They are built following these rules : 1. Any variable x, and the constant cc are λc-terms. 2. If t, u are λc-terms and x is a variable, then (t)u and λx t are λc-terms. 3. If π is a stack, the constant kπ is a λc-term (cal ...
First-order logic;
... each formula Ck is either an axiom in AX or follows from previous formulas using an inference rule in AX : I i.e., there is an inference rule A1 , . . . , An ` B such that Ai = Cji for some ji < N and B = CN . This is said to be a derivation or proof of CN . A derivation is a syntactic object: it’s ...
... each formula Ck is either an axiom in AX or follows from previous formulas using an inference rule in AX : I i.e., there is an inference rule A1 , . . . , An ` B such that Ai = Cji for some ji < N and B = CN . This is said to be a derivation or proof of CN . A derivation is a syntactic object: it’s ...
A(x)
... An are true it holds that the formula B is true as well: A1,…,An |= B: If |=I A1,…, |=I An then |=I B, for all I. Note that the “circumstances“ under which a formula is, or is not, true (see the 1st lesson, Definition 1) are in FOPL modelled by interpretations (of predicates and functional symbols b ...
... An are true it holds that the formula B is true as well: A1,…,An |= B: If |=I A1,…, |=I An then |=I B, for all I. Note that the “circumstances“ under which a formula is, or is not, true (see the 1st lesson, Definition 1) are in FOPL modelled by interpretations (of predicates and functional symbols b ...
