Chapter 2
... Q: you must take the final PQ: If you have more than 9 absences, you must take the final The conditional (if then) statement is true (from your student handbook). So when John Q. Public misses 12 days of school this year, he knows he will have to take the final. [ PQ is true; and P is true (for Jo ...
... Q: you must take the final PQ: If you have more than 9 absences, you must take the final The conditional (if then) statement is true (from your student handbook). So when John Q. Public misses 12 days of school this year, he knows he will have to take the final. [ PQ is true; and P is true (for Jo ...
Nonmonotonic Reasoning - Computer Science Department
... reasoning which is neither a restriction nor an extension of classical logic. Consequences of premises are drawn as much due to the absence as to the presence of knowledge. When more knowledge is acquired, conclusions previously drawn may have to be withdrawn because the rules of inference that led ...
... reasoning which is neither a restriction nor an extension of classical logic. Consequences of premises are drawn as much due to the absence as to the presence of knowledge. When more knowledge is acquired, conclusions previously drawn may have to be withdrawn because the rules of inference that led ...
1 Introduction 2 Formal logic
... Both from philosophical and from practical viewpoints many objections can be raised against the classical interpretation of logic, and many other approaches exist that are more useful than classical logic for certain applications. They will not, however, concern us in these notes. ...
... Both from philosophical and from practical viewpoints many objections can be raised against the classical interpretation of logic, and many other approaches exist that are more useful than classical logic for certain applications. They will not, however, concern us in these notes. ...
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. ...
slides
... ... without having to consider explicitly every store and interpretation! Idea: develop a proof system in which every theorem is a valid partial correctness statement Judgements of the form ⊢ {P} c {Q} De ned inductively using compositional and (mostly) syntax-directed axioms and inference rules ...
... ... without having to consider explicitly every store and interpretation! Idea: develop a proof system in which every theorem is a valid partial correctness statement Judgements of the form ⊢ {P} c {Q} De ned inductively using compositional and (mostly) syntax-directed axioms and inference rules ...
First-Order Logic, Second-Order Logic, and Completeness
... As is well-known, standard semantics is not the only semantics available. Henkin semantics, for example, specifies a second domain of predicates and relations for the upper case constants and variables. The second-order quantifiers binding predicate variables, e.g., can be thought of as ranging over a ...
... As is well-known, standard semantics is not the only semantics available. Henkin semantics, for example, specifies a second domain of predicates and relations for the upper case constants and variables. The second-order quantifiers binding predicate variables, e.g., can be thought of as ranging over a ...
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... agreed on. is is the approach used by cryptographic protocols. One of the earliest applications of knowledge theory in distributed computing was in fault tolerance [ , ]. BAN logics [ ] initiated the la er study, that of epistemic logics for security analysis. is domain poses challenging questions f ...
... agreed on. is is the approach used by cryptographic protocols. One of the earliest applications of knowledge theory in distributed computing was in fault tolerance [ , ]. BAN logics [ ] initiated the la er study, that of epistemic logics for security analysis. is domain poses challenging questions f ...
Logic and Proof
... than yesterday (q). (2) We will go swimming (r) only if it is sunny (p). (3) If we do not go swimming (¬ r), then we will take a canoe trip (s). (4) If we take a canoe trip (s), then we will be home by sunset (t). Therefore, we will be home by sunset (t). (1) ¬ p ∧ q Attention – tricky "only if". Wh ...
... than yesterday (q). (2) We will go swimming (r) only if it is sunny (p). (3) If we do not go swimming (¬ r), then we will take a canoe trip (s). (4) If we take a canoe trip (s), then we will be home by sunset (t). Therefore, we will be home by sunset (t). (1) ¬ p ∧ q Attention – tricky "only if". Wh ...
lecture notes
... 3. If we do not go swimming, then we will take a canoe trip. 4. If we take a canoe trip, then we will be home by sunset. From this hypothesis, we should conclude: We will be home by sunset. We shall come back to it in Example 5. The above conclusions are examples of a syllogisms defined as a “deduct ...
... 3. If we do not go swimming, then we will take a canoe trip. 4. If we take a canoe trip, then we will be home by sunset. From this hypothesis, we should conclude: We will be home by sunset. We shall come back to it in Example 5. The above conclusions are examples of a syllogisms defined as a “deduct ...
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.