T - UTH e
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
First-order logic;
... Representation: Understand the relationships between different representations of the same information or idea. I ...
... Representation: Understand the relationships between different representations of the same information or idea. I ...
L11
... A table of 16 rows is constructed and the truth values of are computed. Since the truth value of is true under all 16 interpretations, it is valid. ...
... A table of 16 rows is constructed and the truth values of are computed. Since the truth value of is true under all 16 interpretations, it is valid. ...
PHILOSOPHY 326 / MATHEMATICS 307 SYMBOLIC LOGIC This
... 114, Introduction to Symbolic Logic, is a prerequisite for Philosophy 326 (or Mathematics 307). It is assumed that all students will have a thorough grasp of the fundamentals of the two-valued logic of propositions – including the fundamental vocabulary of formal deductive logic, the basic two-value ...
... 114, Introduction to Symbolic Logic, is a prerequisite for Philosophy 326 (or Mathematics 307). It is assumed that all students will have a thorough grasp of the fundamentals of the two-valued logic of propositions – including the fundamental vocabulary of formal deductive logic, the basic two-value ...
Notes on Propositional Logic
... leading to the notion of propositional atoms, described in the following section. For traditional logic, we have considered particular forms of arguments that combine propositions. For example, If p1 then p2 . We would like to study in what ways propositions can be combined into arguments, which wil ...
... leading to the notion of propositional atoms, described in the following section. For traditional logic, we have considered particular forms of arguments that combine propositions. For example, If p1 then p2 . We would like to study in what ways propositions can be combined into arguments, which wil ...
PROVING UNPROVABILITY IN SOME NORMAL MODAL LOGIC
... Definition. Let S be a modal logic and S a be a deductive system for a, including L. An Inference in S a is every finite sequence α1 , . . . , αn such that every αi is either an axiom of S a or is obtained form α1 , . . . , αi−1 , the axioms of S a and the theorems of S, accordingly using some of th ...
... Definition. Let S be a modal logic and S a be a deductive system for a, including L. An Inference in S a is every finite sequence α1 , . . . , αn such that every αi is either an axiom of S a or is obtained form α1 , . . . , αi−1 , the axioms of S a and the theorems of S, accordingly using some of th ...
Chapter 1 Section 2
... truth, and knaves, who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” Example: What are the types of A and B? Solution: Let p and q be the statements that A is a knight and B is a knight, respectively. So, then p repres ...
... truth, and knaves, who always lie. You go to the island and meet A and B. A says “B is a knight.” B says “The two of us are of opposite types.” Example: What are the types of A and B? Solution: Let p and q be the statements that A is a knight and B is a knight, respectively. So, then p repres ...
Propositional Logic
... is true not only of resolution, but also for many other calculi. Of the calculi for automated deduction, resolution plays an exceptional role. Thus we wish to work a bit more closely with it. In contrast to other calculi, resolution has only two inference rules, and it works with formulas in conjunc ...
... is true not only of resolution, but also for many other calculi. Of the calculi for automated deduction, resolution plays an exceptional role. Thus we wish to work a bit more closely with it. In contrast to other calculi, resolution has only two inference rules, and it works with formulas in conjunc ...
chapter 16
... — A universal proof (or universal derivation) is an ordered list of sentences in which every sentence is either a premise or is derived from earlier lines (not within a completed subproof) using an inference rule. If we are able to prove Φ(xʹ) where xʹ does not appear free in any line above the univ ...
... — A universal proof (or universal derivation) is an ordered list of sentences in which every sentence is either a premise or is derived from earlier lines (not within a completed subproof) using an inference rule. If we are able to prove Φ(xʹ) where xʹ does not appear free in any line above the univ ...
Modal Logic
... Every atomic proposition p is a member of . If is a member of , so is (¬). If and are members of , so is (). If is a member of , so is (❏). ...
... Every atomic proposition p is a member of . If is a member of , so is (¬). If and are members of , so is (). If is a member of , so is (❏). ...
Predicate logic
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...
Assignment 2, 12 Oct 2015, due 20 Oct 2015
... 1. Let L = (R, F, C) be a finite first-order relational language with F = C = ∅ and let M = (S, ι) be a finite L-structure. Show that there is an L-sentence φM whose models are precisely the L-structures isomorphic to M. 2. (a) Let L = {0, +, ×} where + and × are binary function symbols and 0 is a c ...
... 1. Let L = (R, F, C) be a finite first-order relational language with F = C = ∅ and let M = (S, ι) be a finite L-structure. Show that there is an L-sentence φM whose models are precisely the L-structures isomorphic to M. 2. (a) Let L = {0, +, ×} where + and × are binary function symbols and 0 is a c ...
Chapter1_Parts2
... an equivalent proposition is the disjunction with n disjuncts (where n is the number of rows for which the formula evaluates to T). Each disjunct has m conjuncts where m is the number of distinct propositional variables. Each conjunct includes the positive form of the propositional variable if the v ...
... an equivalent proposition is the disjunction with n disjuncts (where n is the number of rows for which the formula evaluates to T). Each disjunct has m conjuncts where m is the number of distinct propositional variables. Each conjunct includes the positive form of the propositional variable if the v ...
03_Artificial_Intelligence-PredicateLogic
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...
... • Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe) • Valuation – Assigns domain objects to variables – The Valuation function can be used for ...