p - Erwin Sitompul
... Example: Three propositions are given to describe the quality of a hotel. p: “The service is good.” q: “The room rate is low.” r: “The hotel is a three-star hotel.” Translate the following proposition into symbolic notation: i. “The room rate is low but the service is bad.” ii. “Either the room ra ...
... Example: Three propositions are given to describe the quality of a hotel. p: “The service is good.” q: “The room rate is low.” r: “The hotel is a three-star hotel.” Translate the following proposition into symbolic notation: i. “The room rate is low but the service is bad.” ii. “Either the room ra ...
Symbolic Logic I: The Propositional Calculus
... of P . This means that when tv(P ) = 1, then tv(¬P ) = 0, and when tv(P ) = 0, then tv(¬P ) = 1. 2.3. Conjunction. Since P ∧ Q asserts both P and Q, we have tv(P ∧ Q) = 1 when both tv(P ) = 1 and tv(Q) = 1, but tv(P ∧ Q) = 0 otherwise. That is, tv(P ∧ Q) = 0 whenever at least one of tv(P ) = 0 or tv ...
... of P . This means that when tv(P ) = 1, then tv(¬P ) = 0, and when tv(P ) = 0, then tv(¬P ) = 1. 2.3. Conjunction. Since P ∧ Q asserts both P and Q, we have tv(P ∧ Q) = 1 when both tv(P ) = 1 and tv(Q) = 1, but tv(P ∧ Q) = 0 otherwise. That is, tv(P ∧ Q) = 0 whenever at least one of tv(P ) = 0 or tv ...
On Perfect Introspection with Quantifying-in
... To begin with, for expressively weak logics such as propositional logics of belief, our intuitions are indeed captured by the formalisms. For example, in the case of propositional possible-world semantics, Halpern and Moses [HM84], among others, 3 proved that the beliefs of an agent can be reduced t ...
... To begin with, for expressively weak logics such as propositional logics of belief, our intuitions are indeed captured by the formalisms. For example, in the case of propositional possible-world semantics, Halpern and Moses [HM84], among others, 3 proved that the beliefs of an agent can be reduced t ...
A Proof Theory for Generic Judgments
... proof (that is, it can be computed). As we mentioned above, such direct reasoning on logic specification involves instantiations of eigenvariables. Similarly, focusing on their extensional nature guaranteed by cut-elimination, enrichments to the sequent calculus have been proposed by [Hallnäs and S ...
... proof (that is, it can be computed). As we mentioned above, such direct reasoning on logic specification involves instantiations of eigenvariables. Similarly, focusing on their extensional nature guaranteed by cut-elimination, enrichments to the sequent calculus have been proposed by [Hallnäs and S ...
Lecturecise 19 Proofs and Resolution Compactness for
... Inductiveness and the Model Inductive step: Assume the claim for k: every finite subset T ⊆ S has a (v1 , . . . , vk )-interpretation I such that I |= T , we show that the statement holds for k + 1. If vk+1 = false, the inductive statement holds by definition of vk+1 . Let vk+1 = true. Then by defi ...
... Inductiveness and the Model Inductive step: Assume the claim for k: every finite subset T ⊆ S has a (v1 , . . . , vk )-interpretation I such that I |= T , we show that the statement holds for k + 1. If vk+1 = false, the inductive statement holds by definition of vk+1 . Let vk+1 = true. Then by defi ...
Chapter 2, Logic
... gave rise to a good deal of debate among logicians. For sometimes we assert universal generalisations without any commitment to existence. For instance if we explained ‘unicorn’ by saying ‘Unicorn’ means ’quadruped mammal resembling a horse but with a single horn projecting from the middle of its fo ...
... gave rise to a good deal of debate among logicians. For sometimes we assert universal generalisations without any commitment to existence. For instance if we explained ‘unicorn’ by saying ‘Unicorn’ means ’quadruped mammal resembling a horse but with a single horn projecting from the middle of its fo ...
A Brief Introduction to the Intuitionistic Propositional Calculus
... been proposed in the attempt to pin the intuitionists down to a particular logical system, and in consequence typically attempt to formalize some intuitionist’s explanation of their philosophy. This lead to the disquieting understanding that different intuitionists often arrive at, and understand, i ...
... been proposed in the attempt to pin the intuitionists down to a particular logical system, and in consequence typically attempt to formalize some intuitionist’s explanation of their philosophy. This lead to the disquieting understanding that different intuitionists often arrive at, and understand, i ...
A Prologue to the Theory of Deduction
... theory. It makes prominent the proofs t : B—and we think immediately of the marked ones, without hypotheses—while category theory is about the deductions f : A ⊢ B. Logic is concerned not with any deductions, but first of all with formal deductions. Perhaps it is concerned only with such deductions. ...
... theory. It makes prominent the proofs t : B—and we think immediately of the marked ones, without hypotheses—while category theory is about the deductions f : A ⊢ B. Logic is concerned not with any deductions, but first of all with formal deductions. Perhaps it is concerned only with such deductions. ...
Section 2.4: Arguments with Quantified Statements
... of all things in D is contained in Q. Notice however, that it does not tell us whether something in Q is in D (indeed it would be wrong to assume so). In a similar theme, if we have an expression such as ∀x, x ∈ D →∼ Q(x), we would draw two circles representing the domain of D and all the things for ...
... of all things in D is contained in Q. Notice however, that it does not tell us whether something in Q is in D (indeed it would be wrong to assume so). In a similar theme, if we have an expression such as ∀x, x ∈ D →∼ Q(x), we would draw two circles representing the domain of D and all the things for ...
Mathematical Induction - Cambridge Computer Lab
... The left of the sequent is empty, because there are no assumptions. We use the convention that an underlined term is being rewritten to the purple term in the next line. ...
... The left of the sequent is empty, because there are no assumptions. We use the convention that an underlined term is being rewritten to the purple term in the next line. ...
Reasoning in Description Logics with a Concrete Domain in the
... N which is false in I. This case is identical to the one from [3], so we omit the details. Roughly speaking, since is well-founded and total, there is a smallest counterexample C. Furthermore, there is a redundant inference by G D with the main premise C and side premises Ci which are true in I, a ...
... N which is false in I. This case is identical to the one from [3], so we omit the details. Roughly speaking, since is well-founded and total, there is a smallest counterexample C. Furthermore, there is a redundant inference by G D with the main premise C and side premises Ci which are true in I, a ...
How to tell the truth without knowing what you are talking about
... describing what you may not know? The answer is positive provided that the reasoning, from the accepted set of premises to the conclusions, is correct. The problem of verifying whether a reasoning is correct is one of the aims of logic since Aristotle. In particular, modern logic, that is logic sinc ...
... describing what you may not know? The answer is positive provided that the reasoning, from the accepted set of premises to the conclusions, is correct. The problem of verifying whether a reasoning is correct is one of the aims of logic since Aristotle. In particular, modern logic, that is logic sinc ...
Jacques Herbrand (1908 - 1931) Principal writings in logic
... Herbrand domain D(F,p): an arbitrary item, and values for f and g (and any other function signs in R) iterated up to p times. Herbrand (validity) expansion: disjunction of instances of Herbrand functional form over D(F,p): ...
... Herbrand domain D(F,p): an arbitrary item, and values for f and g (and any other function signs in R) iterated up to p times. Herbrand (validity) expansion: disjunction of instances of Herbrand functional form over D(F,p): ...
Logic3
... How to produce additional wffs (sentences) from other ones? What steps can we perform to show that a conclusion follows logically from a set of hypotheses? ...
... How to produce additional wffs (sentences) from other ones? What steps can we perform to show that a conclusion follows logically from a set of hypotheses? ...
A Proof Theory for Generic Judgments: An extended abstract
... need to discover invariants. Another more intensional approach, however, involves introducing a new, generic variable, say, c : γ, that has not been introduced before in the proof, and to prove the formula B[c/x] instead. In natural deduction and sequent calculus proofs, such new variables are calle ...
... need to discover invariants. Another more intensional approach, however, involves introducing a new, generic variable, say, c : γ, that has not been introduced before in the proof, and to prove the formula B[c/x] instead. In natural deduction and sequent calculus proofs, such new variables are calle ...
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.