Chapter 11: Other Logical Tools Syllogisms and Quantification
... logics are the subject of advanced courses, ranging from upper division to high level graduate courses. For the most part, however, they all use propositional logic as a basis or point of departure in the sense of either adding rules or showing contextual restrictions of propositional inferences. ...
... logics are the subject of advanced courses, ranging from upper division to high level graduate courses. For the most part, however, they all use propositional logic as a basis or point of departure in the sense of either adding rules or showing contextual restrictions of propositional inferences. ...
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... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
Logics of Truth - Project Euclid
... to Scott [10] and Aczel [1]. The central notion is AczePs concept of a Frege structure. These structures are models of the Lambda Calculus together with two distinguished subsets —a set of propositions and a subset of this set called truths. In addition, such structures come equipped with the usual ...
... to Scott [10] and Aczel [1]. The central notion is AczePs concept of a Frege structure. These structures are models of the Lambda Calculus together with two distinguished subsets —a set of propositions and a subset of this set called truths. In addition, such structures come equipped with the usual ...
Deductive Reasoning
... • Sherlock Holmes knows that whoever was in the kitchen stole the tomatoes • Sherlock Holmes discovers that Mrs. Hudson was in the kitchen • What can he conclude? ...
... • Sherlock Holmes knows that whoever was in the kitchen stole the tomatoes • Sherlock Holmes discovers that Mrs. Hudson was in the kitchen • What can he conclude? ...
Justification logic with approximate conditional probabilities
... t is a justification term. The first justification logic, the Logic of Proofs, was developed by Artemov [1] with the aim of giving a classical provability interpretation for the modal logic S4 and hence also for intuitionistic logic. The Logic of Proofs interprets justification terms as formal proof ...
... t is a justification term. The first justification logic, the Logic of Proofs, was developed by Artemov [1] with the aim of giving a classical provability interpretation for the modal logic S4 and hence also for intuitionistic logic. The Logic of Proofs interprets justification terms as formal proof ...
lecture notes
... Socrates is a Greek. Therefore, Socrates is a philosopher. This conclusion seems to be perfectly correct, and quite obvious to us. However, we cannot justify it rigorously since we do not have any rule of inference. When the chain of implications is more complicated, as in the example below, a forma ...
... Socrates is a Greek. Therefore, Socrates is a philosopher. This conclusion seems to be perfectly correct, and quite obvious to us. However, we cannot justify it rigorously since we do not have any rule of inference. When the chain of implications is more complicated, as in the example below, a forma ...
Tactical and Strategic Challenges to Logic (KAIST
... to be fruitfully applicable to inconsistent systems that might not be as big as Five Eyes, banking or health-care. Most information-systems that aren’t at all small aren’t big in the Five Eyes sense. All the same, they can be a lot bigger than we might think. The IR project is founded on assumptions ...
... to be fruitfully applicable to inconsistent systems that might not be as big as Five Eyes, banking or health-care. Most information-systems that aren’t at all small aren’t big in the Five Eyes sense. All the same, they can be a lot bigger than we might think. The IR project is founded on assumptions ...
X - Al Akhawayn University
... Only specification of results are stated (not detailed procedures for producing them) ...
... Only specification of results are stated (not detailed procedures for producing them) ...
6.042J Chapter 1: Propositions
... would care whether or not there is a solution to 313.x 3 C y 3 / D z 3 where x, y, and z are positive integers. It turns out that finding solutions to such equations is important in the field of elliptic curves, which turns out to be important to the study of factoring large integers, which turns ou ...
... would care whether or not there is a solution to 313.x 3 C y 3 / D z 3 where x, y, and z are positive integers. It turns out that finding solutions to such equations is important in the field of elliptic curves, which turns out to be important to the study of factoring large integers, which turns ou ...
Monadic Second Order Logic and Automata on Infinite Words
... words and uses the Büchi acceptance condition (defined below). A Büchi automaton A is a tuple hQ, A, q0 , ∆, F i, where Q is the finite set of states, A is the alphabet, q0 ∈ Q is the start state, ∆ ⊆ Q × A × Q is the transition relation, and F ⊆ Q is the set of accept states. A run of A on w is a ...
... words and uses the Büchi acceptance condition (defined below). A Büchi automaton A is a tuple hQ, A, q0 , ∆, F i, where Q is the finite set of states, A is the alphabet, q0 ∈ Q is the start state, ∆ ⊆ Q × A × Q is the transition relation, and F ⊆ Q is the set of accept states. A run of A on w is a ...
Extending modal logic
... This means adding axioms to the logic. The good properties of the basic modal logic may or may not ...
... This means adding axioms to the logic. The good properties of the basic modal logic may or may not ...
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... tableau cannot be extended any further, because all formulas have been decomposed. Since the propositional tableau method terminates after finitely many steps, this was an easy thing to define. In the first-order case, however, we have to be a bit more careful. We know that because of γ-formulas, pr ...
... tableau cannot be extended any further, because all formulas have been decomposed. Since the propositional tableau method terminates after finitely many steps, this was an easy thing to define. In the first-order case, however, we have to be a bit more careful. We know that because of γ-formulas, pr ...
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... Gödel’s incompleteness theorem is often described as “any consistent and sufficiently strong formal theory of arithmetic is incomplete”, where a formal theory is viewed as one whose theorems are derivable from an axiom system. For such theories there will always be formulas that are true (for insta ...
... Gödel’s incompleteness theorem is often described as “any consistent and sufficiently strong formal theory of arithmetic is incomplete”, where a formal theory is viewed as one whose theorems are derivable from an axiom system. For such theories there will always be formulas that are true (for insta ...
CHAPTER 9 Two Proofs of Completeness Theorem 1 Classical
... The soundness theorem proves that our prove system ”produces” only tautologies. We show, as the next step, that our proof system ”produces” not only tautologies, but all of the tautologies. This is called a completeness theorem. The proof of completeness theorem for a given semantics and a given pr ...
... The soundness theorem proves that our prove system ”produces” only tautologies. We show, as the next step, that our proof system ”produces” not only tautologies, but all of the tautologies. This is called a completeness theorem. The proof of completeness theorem for a given semantics and a given pr ...
Object-Based Unawareness
... tries to model agents such as James Iredell has first to express EU sentences. However, RU sentences are not easy to express in traditional economic models such as those based on information partitions. In fact, such models preclude the expression of an even simpler class of sentences, which we shal ...
... tries to model agents such as James Iredell has first to express EU sentences. However, RU sentences are not easy to express in traditional economic models such as those based on information partitions. In fact, such models preclude the expression of an even simpler class of sentences, which we shal ...
Saturation of Sets of General Clauses
... 2. In the proof, it does not really matter with which negative literal an inference is performed ⇒ choose a negative literal don’t-care-nondeterministically ⇒ selection ...
... 2. In the proof, it does not really matter with which negative literal an inference is performed ⇒ choose a negative literal don’t-care-nondeterministically ⇒ selection ...
Philosophy of Language: Wittgenstein
... “The King of France in 2000 is bald” includes the definite description “the King of France in 2000”. The proposition is thus shorthand for “There is at least one thing, x, that is a King of France in 2000, there is at most one thing that is a King of France in 2000, and x is bald”. 2. For Wittgenste ...
... “The King of France in 2000 is bald” includes the definite description “the King of France in 2000”. The proposition is thus shorthand for “There is at least one thing, x, that is a King of France in 2000, there is at most one thing that is a King of France in 2000, and x is bald”. 2. For Wittgenste ...