Resolution Proof System for First Order Logic
... In order to use resolution for first order logic the formulas must be converted into clausal form. A clause is a disjunction of literals with no literal appearing twice, no existential quantifiers and all universal quantifiers are at the left. ...
... In order to use resolution for first order logic the formulas must be converted into clausal form. A clause is a disjunction of literals with no literal appearing twice, no existential quantifiers and all universal quantifiers are at the left. ...
Lecture01 - Mathematics
... proposition. Form is the key word. An expression like p ( q ( p r )) is only a form until actual propositions replace the variables p, q, and r. (just as in arithmetic/algebra an expression like x 2 y 2 is only a form until actual numbers replace the variables x and y). (2) Mathematics often ...
... proposition. Form is the key word. An expression like p ( q ( p r )) is only a form until actual propositions replace the variables p, q, and r. (just as in arithmetic/algebra an expression like x 2 y 2 is only a form until actual numbers replace the variables x and y). (2) Mathematics often ...
Chapter 1 Logic and Set Theory
... A logical implication can be intuitively described as “P implies Q” if Q must be true whenever P is true. That is, Q cannot be false if P is true. Necessity is the key aspect of this sentence, the fact that P and Q both happen to be true cannot be coincidental. To have P implies Q, we need the condi ...
... A logical implication can be intuitively described as “P implies Q” if Q must be true whenever P is true. That is, Q cannot be false if P is true. Necessity is the key aspect of this sentence, the fact that P and Q both happen to be true cannot be coincidental. To have P implies Q, we need the condi ...
MATH 103: Contemporary Mathematics Logic Study Guide
... 2. Review the symbolic notation for negations and compound statements (examples on pages 19-20). You should now know the meaning of the symbols ¬, ∨, ∧, → 3. If a statement is true, then its negation is 4. Review truth values and truth tables. Study the truth tables for p ∨ q, p ∧ q, p → q. You will ...
... 2. Review the symbolic notation for negations and compound statements (examples on pages 19-20). You should now know the meaning of the symbols ¬, ∨, ∧, → 3. If a statement is true, then its negation is 4. Review truth values and truth tables. Study the truth tables for p ∨ q, p ∧ q, p → q. You will ...
Extending modal logic
... Other examples: ternary Kripke models, bi-modal Kripke models, .. Further generalizations of the class of KPFs are possible, covering also, e.g., neighborhood models. ...
... Other examples: ternary Kripke models, bi-modal Kripke models, .. Further generalizations of the class of KPFs are possible, covering also, e.g., neighborhood models. ...
Mathematics for Computer Science/Software Engineering
... S is a partition of A, define a relation R on A by aRb whenever a and b are in the same part of the partition, i.e. whenever there is a set T ∈ S with a ∈ T and b ∈ T . Then we show that R is an equivalence relation. Example: S = {{1, 3, 4}, {5}, {2, 6}}. Conversely, if R is an equivalence relation ...
... S is a partition of A, define a relation R on A by aRb whenever a and b are in the same part of the partition, i.e. whenever there is a set T ∈ S with a ∈ T and b ∈ T . Then we show that R is an equivalence relation. Example: S = {{1, 3, 4}, {5}, {2, 6}}. Conversely, if R is an equivalence relation ...
Jean Van Heijenoort`s View of Modern Logic
... quantification; but this could not be obtained till the traditional decomposition of the proposition into subject and predicate had been replaced by its analysis into function and argument(s). A preliminary accomplishment was the propositional calculus, with a truth-functional definition of the conn ...
... quantification; but this could not be obtained till the traditional decomposition of the proposition into subject and predicate had been replaced by its analysis into function and argument(s). A preliminary accomplishment was the propositional calculus, with a truth-functional definition of the conn ...
(p q r) (p q r) (p q r) (p q r) ( p q r)
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
THE HISTORY OF LOGIC
... overlapping traditions in the development of logic. One of them originates with Boole and includes, among others, Peirce, Jevons, Schröder, and Venn. This ‘algebraic school’ focussed on the relationship between regularities in correct resaoning and operations like addition and multiplication. A pri ...
... overlapping traditions in the development of logic. One of them originates with Boole and includes, among others, Peirce, Jevons, Schröder, and Venn. This ‘algebraic school’ focussed on the relationship between regularities in correct resaoning and operations like addition and multiplication. A pri ...
2.3 Weakest Preconditions
... or “executing S1 ; S2 is guaranteed to make φ true exactly when executing S1 is guaranteed to end in those circumstances, where executing S2 is guaranteed to make φ true”. • Syntactically, GCL follows the Algol 60 and Pascal tradition where ‘;’ is an operator for joining the two commands into one la ...
... or “executing S1 ; S2 is guaranteed to make φ true exactly when executing S1 is guaranteed to end in those circumstances, where executing S2 is guaranteed to make φ true”. • Syntactically, GCL follows the Algol 60 and Pascal tradition where ‘;’ is an operator for joining the two commands into one la ...
Summary - Reasoning and Logic
... Definition: A statement or proposition is a sentence which can be classified as true or false (but not both) without ambiguity. The truth or falsity of the statement is known as the truth value. Example 2 Consider the following sentences: 1. “Every function is differentiable” is a statement with truth ...
... Definition: A statement or proposition is a sentence which can be classified as true or false (but not both) without ambiguity. The truth or falsity of the statement is known as the truth value. Example 2 Consider the following sentences: 1. “Every function is differentiable” is a statement with truth ...
