Basic Metatheory for Propositional, Predicate, and Modal Logic
... formulas — deemed valid by the semantics.1 In this section, we define a formal system of propositional logic (a.k.a. sentential logic or sentence logic). Propositional logic is so-called because the basic meaningful units are propositions, or sentences, such as “John is happy”, or “CSIRO is Australi ...
... formulas — deemed valid by the semantics.1 In this section, we define a formal system of propositional logic (a.k.a. sentential logic or sentence logic). Propositional logic is so-called because the basic meaningful units are propositions, or sentences, such as “John is happy”, or “CSIRO is Australi ...
Propositional/First
... • How can these sentences be represented so that we can infer the third sentence from the first two? ...
... • How can these sentences be represented so that we can infer the third sentence from the first two? ...
PREPOSITIONAL LOGIS
... • How can these sentences be represented so that we can infer the third sentence from the first two? ...
... • How can these sentences be represented so that we can infer the third sentence from the first two? ...
Godel`s Incompleteness Theorem
... Another Trivially Complete Axiom Set • Consider A = {S � LA | N ⊨ S} – Again, clearly, A is complete. Cool! – OK, but this isn’t what we would intuitively consider an ‘axiom set’: it goes against the whole idea of deriving all theorems from a small set of basic and elementary truths. Not cool! – Mo ...
... Another Trivially Complete Axiom Set • Consider A = {S � LA | N ⊨ S} – Again, clearly, A is complete. Cool! – OK, but this isn’t what we would intuitively consider an ‘axiom set’: it goes against the whole idea of deriving all theorems from a small set of basic and elementary truths. Not cool! – Mo ...
ppt
... • Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated • We say m is a model of a sentence α if α is true in m • M(α) is the set of all models of α • Then KB ╞ α iff M(KB) M(α) – E.g. KB = Giants won and Reds won α = Giants ...
... • Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated • We say m is a model of a sentence α if α is true in m • M(α) is the set of all models of α • Then KB ╞ α iff M(KB) M(α) – E.g. KB = Giants won and Reds won α = Giants ...
Chapter 1: The Foundations: Logic and Proofs
... P is a sufficient condition for Q Q if P Q whenever P Q is a necessary condition for P ...
... P is a sufficient condition for Q Q if P Q whenever P Q is a necessary condition for P ...
Lecture 3 - CSE@IIT Delhi
... An argument is a sequence of statements. All statements but the final one are called assumptions or hypothesis. The final statement is called the conclusion. An argument is valid if: whenever all the assumptions are true, then the conclusion is true. If today is Wednesday, then yesterday was Tuesday ...
... An argument is a sequence of statements. All statements but the final one are called assumptions or hypothesis. The final statement is called the conclusion. An argument is valid if: whenever all the assumptions are true, then the conclusion is true. If today is Wednesday, then yesterday was Tuesday ...
Higher-Order Modal Logic—A Sketch
... Sometimes it is helpful to refer to the order of a term or formula—first-order, second-order, and so on. Types will play the fundamental role, but order provides a convenient way of referring to the maximum complexity of some construct. Definition 2 (Order). The type 0 is of order 0. And if each of ...
... Sometimes it is helpful to refer to the order of a term or formula—first-order, second-order, and so on. Types will play the fundamental role, but order provides a convenient way of referring to the maximum complexity of some construct. Definition 2 (Order). The type 0 is of order 0. And if each of ...
pdf
... the Φ if it is clear from context or does not play a significant role.) As usual, we define ϕ∨ψ and ϕ ⇒ ψ as abbreviations of ¬(¬ϕ ∧ ¬ψ) and ¬ϕ ∨ ψ, respectively. The intended interpretation of Kϕ varies depending on the context. It typically has been interpreted as knowledge, as belief, or as neces ...
... the Φ if it is clear from context or does not play a significant role.) As usual, we define ϕ∨ψ and ϕ ⇒ ψ as abbreviations of ¬(¬ϕ ∧ ¬ψ) and ¬ϕ ∨ ψ, respectively. The intended interpretation of Kϕ varies depending on the context. It typically has been interpreted as knowledge, as belief, or as neces ...
Logic - United States Naval Academy
... Two (compound) expressions are logically equivalent if and only if they have identical truth values for all possible combinations of truth values for the sub-expressions. If A and B are logically equivalent, we write A B . (Another notation for logical equivalence is ; that is, if A and B are lo ...
... Two (compound) expressions are logically equivalent if and only if they have identical truth values for all possible combinations of truth values for the sub-expressions. If A and B are logically equivalent, we write A B . (Another notation for logical equivalence is ; that is, if A and B are lo ...
Modal Logics Definable by Universal Three
... Thus we may think that every modal formula ϕ defines a class of frames, namely the class of those frames in which ϕ is valid. A formula ϕ is valid in a frame K if for any possible truth-assignment of propositional variables to the worlds of K, ϕ is true at every world. While this definition involves ...
... Thus we may think that every modal formula ϕ defines a class of frames, namely the class of those frames in which ϕ is valid. A formula ϕ is valid in a frame K if for any possible truth-assignment of propositional variables to the worlds of K, ϕ is true at every world. While this definition involves ...
Multi-Agent Only
... If Alice believes that all that Bob knows is that birds normally fly and that Tweety is a bird, then Alice believes that Bob believes that Tweety flies. But technically things were surprisingly cumbersome! The problem lies in the complexity in what agents consider ...
... If Alice believes that all that Bob knows is that birds normally fly and that Tweety is a bird, then Alice believes that Bob believes that Tweety flies. But technically things were surprisingly cumbersome! The problem lies in the complexity in what agents consider ...
2/TRUTH-FUNCTIONS
... ForclassDiscussionsOnly.Teacher.Armand.L.Tan.AssociateProfessor. PhilosophyDepartment.SillimanUniversity s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement ...
... ForclassDiscussionsOnly.Teacher.Armand.L.Tan.AssociateProfessor. PhilosophyDepartment.SillimanUniversity s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement ...
Partial Correctness Specification
... A proof in Floyd-Hoare logic is a sequence of lines, each of which is either an axiom of the logic or follows from earlier lines by a rule of inference of the logic u ...
... A proof in Floyd-Hoare logic is a sequence of lines, each of which is either an axiom of the logic or follows from earlier lines by a rule of inference of the logic u ...
ws2 - Seeing this instead of the website you expected?
... Either government taxes will go up or inflation will go up. Inflation will not go up. So, government taxes will go up. 8. Is the following argument valid? France will go to war with Italy only if India and Japan both invade Russia. France will go to war with Italy. ...
... Either government taxes will go up or inflation will go up. Inflation will not go up. So, government taxes will go up. 8. Is the following argument valid? France will go to war with Italy only if India and Japan both invade Russia. France will go to war with Italy. ...
Sentential Logic 2 - Michael Johnson's Homepage
... We say that an argument is deductively valid when it has the following property: If the premises of the argument are true, then the conclusion of the argument must be true. A valid argument is “truth-preserving”: the truth of the premises gets passed on to the ...
... We say that an argument is deductively valid when it has the following property: If the premises of the argument are true, then the conclusion of the argument must be true. A valid argument is “truth-preserving”: the truth of the premises gets passed on to the ...