Homework #5
... 1. Note to yourself that the following are valid for intuitionistic logic. (a) ` (A ∧ B) ↔ (B ∧ A) (b) ` (A ∨ B) ↔ (B ∨ A) (c) ` (A ∨ (B ∨ C)) ↔ ((A ∨ B) ∨ C) (d) ` (A ∧ (B ∧ C)) ↔ ((A ∧ B) ∧ C) (e) ` (A ∧ (B ∨ C)) ↔ ((A ∧ B) ∨ (A ∧ C)) (f) ` (A ∨ (B ∧ C)) ↔ ((A ∨ B) ∧ (A ∨ C)) (g) ` (A → (B → C)) ↔ ...
... 1. Note to yourself that the following are valid for intuitionistic logic. (a) ` (A ∧ B) ↔ (B ∧ A) (b) ` (A ∨ B) ↔ (B ∨ A) (c) ` (A ∨ (B ∨ C)) ↔ ((A ∨ B) ∨ C) (d) ` (A ∧ (B ∧ C)) ↔ ((A ∧ B) ∧ C) (e) ` (A ∧ (B ∨ C)) ↔ ((A ∧ B) ∨ (A ∧ C)) (f) ` (A ∨ (B ∧ C)) ↔ ((A ∨ B) ∧ (A ∨ C)) (g) ` (A → (B → C)) ↔ ...
The Non-Euclidean Revolution Material Axiomatic Systems and the
... The Non-Euclidean Revolution Material Axiomatic Systems and the Turtle Club Example Recall that a material axiomatic system consists of four parts: the primitive (or undefined) terms, the defined terms, the axioms (or assumptions) used as the starting point for deduction, and the theorems (or statem ...
... The Non-Euclidean Revolution Material Axiomatic Systems and the Turtle Club Example Recall that a material axiomatic system consists of four parts: the primitive (or undefined) terms, the defined terms, the axioms (or assumptions) used as the starting point for deduction, and the theorems (or statem ...
On Herbrand`s Theorem for Intuitionistic Logic
... to the deducibility of a Herbrand extension, and then the necessary Herbrand terms can be extracted from the cut-free proof. In fact, a similar idea is used in free-variable tableau methods [8], where quantifiers are dealt with separately from dealing with the propositional proof skeleton. Since fre ...
... to the deducibility of a Herbrand extension, and then the necessary Herbrand terms can be extracted from the cut-free proof. In fact, a similar idea is used in free-variable tableau methods [8], where quantifiers are dealt with separately from dealing with the propositional proof skeleton. Since fre ...
Comp 371 Fall 2005 Assignment 1
... Due for the late submission with 10% penalty: 11:59 PM, October 23, 2016 ...
... Due for the late submission with 10% penalty: 11:59 PM, October 23, 2016 ...
First Order Predicate Logic
... A path in a tableaux is contradictory or closed if some atomic formulae α and ~ α appear on the same path. If all the paths of a tableau are closed, then it is called a contradictory tableaux. A tableau proof of a formula α is a contradictory tableau with root as ~ α . Let α be any formula. If table ...
... A path in a tableaux is contradictory or closed if some atomic formulae α and ~ α appear on the same path. If all the paths of a tableau are closed, then it is called a contradictory tableaux. A tableau proof of a formula α is a contradictory tableau with root as ~ α . Let α be any formula. If table ...
Propositional Logic What is logic? Propositions Negation
... – If p is the proposition “ISE students love logic”, and q is the proposition “ISE students are crazy”, then – p ∧ q is the proposition “ISE students love logic and are crazy” – p ∨ q is the proposition “ISE students either love logic, or are crazy, or both” Note the syntax is different to that used ...
... – If p is the proposition “ISE students love logic”, and q is the proposition “ISE students are crazy”, then – p ∧ q is the proposition “ISE students love logic and are crazy” – p ∨ q is the proposition “ISE students either love logic, or are crazy, or both” Note the syntax is different to that used ...
Logical Implications
... The conditional if-then used in several programming languages should not be confused with logical implications. Suppose we encounter if p then S in some programming language, the statement S will be executed if p is true. If p is false, statement S will not be executed. In general, S is not a statem ...
... The conditional if-then used in several programming languages should not be confused with logical implications. Suppose we encounter if p then S in some programming language, the statement S will be executed if p is true. If p is false, statement S will not be executed. In general, S is not a statem ...
Document
... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
PDF
... In this entry, we will prove the substitution theorem for propositional logic based on the axiom system found here. Besides the deduction theorem, below are some additional results we will need to prove the theorem: 1. If ∆ ` A → B and Γ ` B → C, then ∆, Γ ` A → C. 2. ∆ ` A and ∆ ` B iff ∆ ` A ∧ B. ...
... In this entry, we will prove the substitution theorem for propositional logic based on the axiom system found here. Besides the deduction theorem, below are some additional results we will need to prove the theorem: 1. If ∆ ` A → B and Γ ` B → C, then ∆, Γ ` A → C. 2. ∆ ` A and ∆ ` B iff ∆ ` A ∧ B. ...
Completeness through Flatness in Two
... of a model should be a full square. The theory of such relativized squares may be both decidable and nicely axiomatizable (cf. Marx et alii [15] for some examples). For the axiomatizability problem, a different solution was found by Gabbay (cf. [3]); by introducing so-called irreflexivity rules, var ...
... of a model should be a full square. The theory of such relativized squares may be both decidable and nicely axiomatizable (cf. Marx et alii [15] for some examples). For the axiomatizability problem, a different solution was found by Gabbay (cf. [3]); by introducing so-called irreflexivity rules, var ...
Structural Multi-type Sequent Calculus for Inquisitive Logic
... We write φ |= ψ if, for any state S , if S |= φ then S |= ψ. If both φ |= ψ and ψ |= φ, then we write φ ≡ ψ. An InqL-formula φ is valid, denoted |= φ, if S |= φ for any state S . The logic InqL is the set of all valid InqL-formulas. An easy inductive proof shows that InqL-formulas have the downward ...
... We write φ |= ψ if, for any state S , if S |= φ then S |= ψ. If both φ |= ψ and ψ |= φ, then we write φ ≡ ψ. An InqL-formula φ is valid, denoted |= φ, if S |= φ for any state S . The logic InqL is the set of all valid InqL-formulas. An easy inductive proof shows that InqL-formulas have the downward ...
Propositional Logic, Predicates, and Equivalence
... to solve a problem involving compound interest. The topic of integer sequences is covered, which requires more critical and creative thinking than the other material. Examples 1215 involve conjecturing a formula or rule for generating the terms of a sequence when only the first few terms are known. ...
... to solve a problem involving compound interest. The topic of integer sequences is covered, which requires more critical and creative thinking than the other material. Examples 1215 involve conjecturing a formula or rule for generating the terms of a sequence when only the first few terms are known. ...