Chapter 2, Logic
... What is Philosophy Chapter 2 by Richard Thompson gave rise to a good deal of debate among logicians. For sometimes we assert universal generalisations without any commitment to existence. For instance if we explained ‘unicorn’ by saying ‘Unicorn’ means ’quadruped mammal resembling a horse but with ...
... What is Philosophy Chapter 2 by Richard Thompson gave rise to a good deal of debate among logicians. For sometimes we assert universal generalisations without any commitment to existence. For instance if we explained ‘unicorn’ by saying ‘Unicorn’ means ’quadruped mammal resembling a horse but with ...
Formal deduction in propositional logic
... syntactic one, that is, we give formal rules for deduction which are purely syntactical. • We want to define a relation called formal deducibility to allow us to mechanically check the validity of a proof. • The significance of the word formal will be explained later. The important point is that for ...
... syntactic one, that is, we give formal rules for deduction which are purely syntactical. • We want to define a relation called formal deducibility to allow us to mechanically check the validity of a proof. • The significance of the word formal will be explained later. The important point is that for ...
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... and one can eliminate the use of 1 by using 1 = 20 . More formally we define: Definition Let n ∈ ω . The extended base k notation for n is inductively defined as follows. The expression 0 is the extended base k notation for n = 0. For n > 0, write n in base k notation as n = kn1 · a1 + · · · + kn` · ...
... and one can eliminate the use of 1 by using 1 = 20 . More formally we define: Definition Let n ∈ ω . The extended base k notation for n is inductively defined as follows. The expression 0 is the extended base k notation for n = 0. For n > 0, write n in base k notation as n = kn1 · a1 + · · · + kn` · ...
CHAPTER 1 The main subject of Mathematical Logic is
... For the human reader such representations are less convenient, so we shall stick to the use of bound variables. In the definition of “substitution of expression E 0 for variable x in expression E”, either one requires that no variable free in E 0 becomes bound by a variable-binding operator in E, wh ...
... For the human reader such representations are less convenient, so we shall stick to the use of bound variables. In the definition of “substitution of expression E 0 for variable x in expression E”, either one requires that no variable free in E 0 becomes bound by a variable-binding operator in E, wh ...
Q 0 - SSDI
... If an infinite branch is to the “left” of any success node, the “left to right depth first search” of Prolog does not succeed (no termination). ...
... If an infinite branch is to the “left” of any success node, the “left to right depth first search” of Prolog does not succeed (no termination). ...
The Complexity of Local Stratification - SUrface
... to be used. Call the finite-register machine programs determined by the above choice instruction together with the standard finite-register machine instructions nondeterministic finite-register machine programs. Operationally, the choice instruction nondeterministically assigns a natural number to X ...
... to be used. Call the finite-register machine programs determined by the above choice instruction together with the standard finite-register machine instructions nondeterministic finite-register machine programs. Operationally, the choice instruction nondeterministically assigns a natural number to X ...
Kripke completeness revisited
... excessive use of “intuitive” arguments on the geometry of tableau proofs. Kaplan suggested a different, more “mathematical” and more elegant approach based on an adaptation of Henkin’s completeness proof for classical logic. Indeed, a Henkin-style completeness proof for S5 had already been published ...
... excessive use of “intuitive” arguments on the geometry of tableau proofs. Kaplan suggested a different, more “mathematical” and more elegant approach based on an adaptation of Henkin’s completeness proof for classical logic. Indeed, a Henkin-style completeness proof for S5 had already been published ...
CptS 440 / 540 Artificial Intelligence
... • If not sure which of two squares have a pit and must enter one of them to reach the gold, the agent will take a chance • If can only act with certainty, most of the time will not act. Consider example that agent wants to drive someone to the airport to catch a flight, and is considering plan A90 t ...
... • If not sure which of two squares have a pit and must enter one of them to reach the gold, the agent will take a chance • If can only act with certainty, most of the time will not act. Consider example that agent wants to drive someone to the airport to catch a flight, and is considering plan A90 t ...
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... We briefly review the five standard systems of reverse mathematics. For completeness, we include systems stronger than arithmetical comprehension, but these will play no part in this paper. Details, general background, and results, as well as many examples of reversals, can be found in Simpson [1999 ...
... We briefly review the five standard systems of reverse mathematics. For completeness, we include systems stronger than arithmetical comprehension, but these will play no part in this paper. Details, general background, and results, as well as many examples of reversals, can be found in Simpson [1999 ...
Completeness and Decidability of a Fragment of Duration Calculus
... Duration Calculus (DC) was introduced by Zhou, Hoare and Ravn in 1991 as a logic to specify the requirements for real-time systems. DC has been used successfully in many case studies, see e.g. [ZZ94,YWZP94,HZ94,DW94,BHCZ94,XH95], [Dan98,ED99]. In [DW94], we have developed a method for designing a re ...
... Duration Calculus (DC) was introduced by Zhou, Hoare and Ravn in 1991 as a logic to specify the requirements for real-time systems. DC has been used successfully in many case studies, see e.g. [ZZ94,YWZP94,HZ94,DW94,BHCZ94,XH95], [Dan98,ED99]. In [DW94], we have developed a method for designing a re ...
Belief closure: A semantics of common knowledge for
... partitions, and then explains that this definition can be rephrased into more intuitive terms, using the notion of a 'reachable' state of the world. Very roughly speaking, definition 1 is of the circular kind, and definition 2 of the iterate kind. However, in view of the immediate mathematical equiv ...
... partitions, and then explains that this definition can be rephrased into more intuitive terms, using the notion of a 'reachable' state of the world. Very roughly speaking, definition 1 is of the circular kind, and definition 2 of the iterate kind. However, in view of the immediate mathematical equiv ...