A Critique of the Foundations of Hoare-Style Programming Logics
... Proof rules for programs with conditional and while Consider a programming language with simple assignments x := E ...
... Proof rules for programs with conditional and while Consider a programming language with simple assignments x := E ...
Logical Argument
... Converse Fallacy of Accident. To argue from a special case to a general rule; a deductive fallacy that can occur when an exception to a generalization is wrongly called for. For example: If we allow people with glaucoma to use medical marijuana then everyone should be allowed to use marijuana. Peopl ...
... Converse Fallacy of Accident. To argue from a special case to a general rule; a deductive fallacy that can occur when an exception to a generalization is wrongly called for. For example: If we allow people with glaucoma to use medical marijuana then everyone should be allowed to use marijuana. Peopl ...
A Critique of the Foundations of Hoare-Style
... Proof rules for programs with conditional and while Consider a programming language with simple assignments x := E ...
... Proof rules for programs with conditional and while Consider a programming language with simple assignments x := E ...
Systems of modal logic - Department of Computing
... a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilber ...
... a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Which closure conditions? See below. Systems of modal logic can also be defined (syntactically) in other ways, usually by reference to some kind of proof system. For example: • Hilber ...
MATH 103: Contemporary Mathematics Logic Study Guide
... 19. Venn (Euler) diagrams are used to determine the validity of “categorical syllogisms” (arguments involving quantifiers, i.e. words such as all, some, none, etc.). Read about these in Section 2.9. 20. Complete this definition: “An argument is valid when, whenever ALL premises are true, then . . . ...
... 19. Venn (Euler) diagrams are used to determine the validity of “categorical syllogisms” (arguments involving quantifiers, i.e. words such as all, some, none, etc.). Read about these in Section 2.9. 20. Complete this definition: “An argument is valid when, whenever ALL premises are true, then . . . ...
CHAPTER 1 INTRODUCTION 1 Mathematical Paradoxes
... is not looked upon as a closed whole. It is infinite in a sense that to any given finite set of positive integers it is always possible to add one more positive integer. The notion of the set of all subsets of the set of all positive integers is not regarded meaningful. Obviously, intuitionists’ vie ...
... is not looked upon as a closed whole. It is infinite in a sense that to any given finite set of positive integers it is always possible to add one more positive integer. The notion of the set of all subsets of the set of all positive integers is not regarded meaningful. Obviously, intuitionists’ vie ...
POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
Everything is Knowable - Computer Science Intranet
... well-known postulate describes that if you revise a theory (set of formulas) with novel information described in a proposition p, then p should after that revision process form part of the theory, it should be believed! This postulate is called the success postulate. Initially, belief revision had n ...
... well-known postulate describes that if you revise a theory (set of formulas) with novel information described in a proposition p, then p should after that revision process form part of the theory, it should be believed! This postulate is called the success postulate. Initially, belief revision had n ...
Propositional Logic - Department of Computer Science
... • Soundness: If there exists a complete tableau path S0 , S1 , . . . , Sn with {P } = S0 and without clash, then P is satisfiable. • Completeness: If P is satisfiable, then no tableau path (generated by the three rules above) S0 , S1 , . . . , Sn with {P } = S0 contains a clash. For the proof, we re ...
... • Soundness: If there exists a complete tableau path S0 , S1 , . . . , Sn with {P } = S0 and without clash, then P is satisfiable. • Completeness: If P is satisfiable, then no tableau path (generated by the three rules above) S0 , S1 , . . . , Sn with {P } = S0 contains a clash. For the proof, we re ...
Logic and Reasoning
... • If KB entails S, then there should be a sequence of inferences through resolution that will lead to at least one clause that cannot be satisfied by any model • Idea: Keep apply resolution to all the pairs of clauses in KB ^ ¬S until: – We can’t find anymore clauses to resolve KB does not entail ...
... • If KB entails S, then there should be a sequence of inferences through resolution that will lead to at least one clause that cannot be satisfied by any model • Idea: Keep apply resolution to all the pairs of clauses in KB ^ ¬S until: – We can’t find anymore clauses to resolve KB does not entail ...
MATH20302 Propositional Logic
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
The Taming of the (X)OR
... satz [Li99] degraded as soon as formulae containing exclusive-or appeared in the original formulation. Thus, solving real crypto-problems with CNF-provers looks unlikely. A similar situation is found in circuit verification where the usage of successful BDD-packages [BRB90] has proven to be utterly ...
... satz [Li99] degraded as soon as formulae containing exclusive-or appeared in the original formulation. Thus, solving real crypto-problems with CNF-provers looks unlikely. A similar situation is found in circuit verification where the usage of successful BDD-packages [BRB90] has proven to be utterly ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
