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Journal of Symbolic Logic, 1965
We consider some natural deduction systems for quantification theory whose only quantificational rules involve elimination of quantifiers. By imposing certain restrictions on the rules, we obtain a system which we term Analytic Natural Deduction; it has the property that the only formulas used in the proof of a given formula X are either subformulas of
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We consider some natural deduction systems for quantification theory whose only quantificational rules involve elimination of quantifiers. By imposing certain restrictions on the rules, we obtain a system which we term Analytic Natural Deduction; it has the property that the only formulas used in the proof of a given formula X are either subformulas of
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1997
Abstract Axiomatic proofs are hard to construct, and often very lengthy. So in practice one does not actually construct such proofs; rather, one proves that there is a proof, as originally defined. One way in which we make use of this technique is when we allow ourselves to use, in a proof, any theorem that has been proved already.
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Abstract Axiomatic proofs are hard to construct, and often very lengthy. So in practice one does not actually construct such proofs; rather, one proves that there is a proof, as originally defined. One way in which we make use of this technique is when we allow ourselves to use, in a proof, any theorem that has been proved already.
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2007
Abstract In this course we shall study some ways of proving statements. Of course not every statement can be proved; so we need to analyse the statements before we prove them. Within propositional logic we analyse complex statements down into shorter statements. Later chapters will analyse statements into smaller expressions too, but the
Ian Chiswell, Wilfrid Hodges
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Abstract In this course we shall study some ways of proving statements. Of course not every statement can be proved; so we need to analyse the statements before we prove them. Within propositional logic we analyse complex statements down into shorter statements. Later chapters will analyse statements into smaller expressions too, but the
Ian Chiswell, Wilfrid Hodges
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Journal of Symbolic Logic, 1950
For Gentzen's natural deduction, a formalized method of deduction in quantification theory dating from 1934, these important advantages may be claimed: it corresponds more closely than other methods of formalized quantification theory to habitual unformalized modes of reasoning, and it consequently tends to minimize the false moves involved in seeking ...
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For Gentzen's natural deduction, a formalized method of deduction in quantification theory dating from 1934, these important advantages may be claimed: it corresponds more closely than other methods of formalized quantification theory to habitual unformalized modes of reasoning, and it consequently tends to minimize the false moves involved in seeking ...
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2010
Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction
Brock-Nannestad, Taus +1 more
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Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction
Brock-Nannestad, Taus +1 more
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2010
This Chapter is devoted to the description of standard systems of natural deduction (ND). After historical introduction in Section 2.1 we present some preliminary criteria which should be satisfied by any system of natural deduction. Sections 2.3 and 2.4 develop a systematization of existing systems based on two features: the kind of data used by a ...
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This Chapter is devoted to the description of standard systems of natural deduction (ND). After historical introduction in Section 2.1 we present some preliminary criteria which should be satisfied by any system of natural deduction. Sections 2.3 and 2.4 develop a systematization of existing systems based on two features: the kind of data used by a ...
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2010
In this Chapter there is a continual emphasis on the application of ND as a tool of proof search and possibly of automation. In particular, we take up the question of how to make ND a universal system. In order to find satisfactory solutions we compare ND with other types of DS’s.
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In this Chapter there is a continual emphasis on the application of ND as a tool of proof search and possibly of automation. In particular, we take up the question of how to make ND a universal system. In order to find satisfactory solutions we compare ND with other types of DS’s.
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Natural Deduction for Hybrid Logic
Journal of Logic and Computation, 2004In this paper, the author studies a natural deduction calculus for hybrid logic. The underlying language contains satisfaction operators \(\forall_a\) as well as binders \(\forall a\) and \(\downarrow a\), where \(a\) is any nominal. It turns out that certain first-order properties of the involved accessibility relation, originating from so-called ...
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Natural Deduction and Curry's Paradox
Journal of Philosophical Logic, 2006Following Fitch, the author presents a natural deduction version of Curry's paradox, a well-known set-theoretic paradox that does not involve negation. She then discusses various restrictions proposed independently by Fitch and Prawitz to prevent the derivation of the paradox.
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1991
This chapter demonstrates how the general theory of partitioned representations can be applied to some specific knowledge representation problems. It will be seen how the theory generalizes some existing AI knowledge representation systems, as well as some systems of logic. In particular, we will look at natural deduction, representing time and action,
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This chapter demonstrates how the general theory of partitioned representations can be applied to some specific knowledge representation problems. It will be seen how the theory generalizes some existing AI knowledge representation systems, as well as some systems of logic. In particular, we will look at natural deduction, representing time and action,
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