Classical Logic and the Curry–Howard Correspondence
... proceed line by line, with each line derived from those preceding it by means of some inference rule. Nowadays such logics are known as ‘Hilbert systems’. This format can be somewhat cumbersome and inelegant, both because it does not follow the reasoning-patterns of ordinary mathematics and because ...
... proceed line by line, with each line derived from those preceding it by means of some inference rule. Nowadays such logics are known as ‘Hilbert systems’. This format can be somewhat cumbersome and inelegant, both because it does not follow the reasoning-patterns of ordinary mathematics and because ...
Partial Correctness Specification
... Later you will be able to prove that these programs are “correct” The postcondition “Y=max(X,Y)” says “Y is the maximum of X and Y in the final state” ...
... Later you will be able to prove that these programs are “correct” The postcondition “Y=max(X,Y)” says “Y is the maximum of X and Y in the final state” ...
lec5 - Indian Institute of Technology Kharagpur
... • If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. • If the unicorn is either immortal or a mammal, then it is horned. • The unicorn is magical if it is horned Can we prove that the unicorn is mythical? Magical? Horned? ...
... • If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. • If the unicorn is either immortal or a mammal, then it is horned. • The unicorn is magical if it is horned Can we prove that the unicorn is mythical? Magical? Horned? ...
Logic of Natural Language Semantics: Presuppositions and
... d. CIs are logically and compositionally independent of what is ‘said (in the favored sense)’, i.e. independent of the at-issue entailments. In this talk, I mainly present Potts (2005) that shows a range of different empirical phenomena such as expressive expressions, appositive nominals (ANs) or ap ...
... d. CIs are logically and compositionally independent of what is ‘said (in the favored sense)’, i.e. independent of the at-issue entailments. In this talk, I mainly present Potts (2005) that shows a range of different empirical phenomena such as expressive expressions, appositive nominals (ANs) or ap ...
Predicate logic. Formal and informal proofs
... Methods of proving theorems Basic methods to prove the theorems: • Direct proof – p q is proved by showing that if p is true then q follows • Indirect proof – Show the contrapositive ¬q ¬p. If ¬q holds then ¬p follows • Proof by contradiction – Show that (p ¬ q) contradicts the assumptions • ...
... Methods of proving theorems Basic methods to prove the theorems: • Direct proof – p q is proved by showing that if p is true then q follows • Indirect proof – Show the contrapositive ¬q ¬p. If ¬q holds then ¬p follows • Proof by contradiction – Show that (p ¬ q) contradicts the assumptions • ...
Propositional Logic Proof
... propositional logic statement, (2) each statement is a premise or follows unequivocally by a previously established rule of inference from the truth of previous statements, and (3) the last statement is the conclusion. A very constrained form of proof, but a good starting point. Interesting proofs w ...
... propositional logic statement, (2) each statement is a premise or follows unequivocally by a previously established rule of inference from the truth of previous statements, and (3) the last statement is the conclusion. A very constrained form of proof, but a good starting point. Interesting proofs w ...
Lesson 12
... is often computationally expensive. Notice that even if inference is not complete it is desirable that it is sound. Propositional Logic and Predicate Logic each with Modus Ponens as their inference produce are sound but not complete. We shall see that we need further (sound) rules of inference to ac ...
... is often computationally expensive. Notice that even if inference is not complete it is desirable that it is sound. Propositional Logic and Predicate Logic each with Modus Ponens as their inference produce are sound but not complete. We shall see that we need further (sound) rules of inference to ac ...
Introduction to Discrete Mathematics
... •To be familiar with formal mathematical reasoning, e.g. logic, proofs •To improve problem solving skills •To see the connections between discrete mathematics and computer science ...
... •To be familiar with formal mathematical reasoning, e.g. logic, proofs •To improve problem solving skills •To see the connections between discrete mathematics and computer science ...
T - RTU
... An inference rule is sound, if the conclusion is true in all cases where the premises are true. To prove the soundness, the truth table must be constructed with one line for each possible model of the proposition symbols in the premises. In all models where the premise is true, the conclusion must b ...
... An inference rule is sound, if the conclusion is true in all cases where the premises are true. To prove the soundness, the truth table must be constructed with one line for each possible model of the proposition symbols in the premises. In all models where the premise is true, the conclusion must b ...
Logic
... • Euclidean: Given a line L and a point P not on L, there is exactly one line passing through P, parallel to L. • Hyperbolic: Given a line L and a point P not on L, there are at least two lines passing through P, parallel to L. • Elliptic: Given a line L and a point P not on L, there are no lines pa ...
... • Euclidean: Given a line L and a point P not on L, there is exactly one line passing through P, parallel to L. • Hyperbolic: Given a line L and a point P not on L, there are at least two lines passing through P, parallel to L. • Elliptic: Given a line L and a point P not on L, there are no lines pa ...
Lecture 3
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
... • “If you clean the car then you can go out” • Could we infer either of the following? – “if you don't clean the car then you can't go out” or – “if you were allowed out, then you must have cleaned the car”. ...
A Brief Introduction to the Intuitionistic Propositional Calculus
... consists of a proof of ϕ together with a proof of ψ, a proof of ϕ ∨ ψ consists of a proof of ϕ or a proof of ψ, while a proof of ϕ ⇒ ψ consists of an algorithm that converts proofs of ϕ into proofs of ψ. For an intuitionist, a propositional formula is a tautology if it can be proven, e.g., α ⇒ α is ...
... consists of a proof of ϕ together with a proof of ψ, a proof of ϕ ∨ ψ consists of a proof of ϕ or a proof of ψ, while a proof of ϕ ⇒ ψ consists of an algorithm that converts proofs of ϕ into proofs of ψ. For an intuitionist, a propositional formula is a tautology if it can be proven, e.g., α ⇒ α is ...
College Geometry University of Memphis MATH 3581 Mathematical
... Proposition: Technically, any statement which has one of two values, True or False. However, the term “proposition” is also used to refer to a theorem (see below). Propositions may be thought of as the preliminary theory which follows from the axioms and postulates and are used to create more compli ...
... Proposition: Technically, any statement which has one of two values, True or False. However, the term “proposition” is also used to refer to a theorem (see below). Propositions may be thought of as the preliminary theory which follows from the axioms and postulates and are used to create more compli ...
Introduction to Proofs, Rules of Equivalence, Rules of
... number of rows in a truth table increases exponentially. R = 2n where n is the number of variables). • Truth tables work only for sentential logic. ...
... number of rows in a truth table increases exponentially. R = 2n where n is the number of variables). • Truth tables work only for sentential logic. ...