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Improving legibility of natural deduction proofs is not trivial [PDF]
Logical Methods in Computer Science, 2014 In formal proof checking environments such as Mizar it is not merely the validity of mathematical formulas that is evaluated in the process of adoption to the body of accepted formalizations, but also the readability of the proofs that witness validity ...
Karol Pąk
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Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts
Bulletin of the Section of Logic, 2022 This paper is about non-labelled proof-systems for hybrid logic, that is, proofsystems where arbitrary formulas can occur, not just satisfaction statements.
Torben Braüner
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Natural deduction calculus for computation tree logic [PDF]
, 2006 We present a natural deduction calculus for the computation tree logic CTL defined with the full set of classical and temporal logic operators. The system extends the natural deduction construction of the linear-time temporal logic.
Bolotov, A. +5 more
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Natural Deduction and Normalization Proofs for the Intersection Type Discipline [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 Refining and extending previous work by Retoré, we develop a systematic approach to intersection types via natural deduction. We show how a step of beta reduction can be seen as performing, at the level of typing derivations, Prawitz reductions in ...
Federico Aschieri
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A Review of Ayatollah Sayyid Muhammad Baqir al-Sadr's Philosophy of History: An Analysis of Inductive Methodology in Discovering Divine Historical Laws [PDF]
تاریخ نگری و تاریخ نگاری, 2023 This paper examines Ayatollah Sayyid Muhammad Baqir al-Sadr's perspective on history through methodological and substantive point of view. In Iqtisaduna (Our Economy), Sadr argues that the inductive laboratory methods used in the natural sciences cannot ...
Zahra AlhooiiNazari, Elham Rabiee
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A natural extension of natural deduction [PDF]
Journal of Symbolic Logic, 1984 One of the main ideas of calculi of natural deduction, as introduced by Jaśkowski and Gentzen, is that assumptions may be discharged in the course of a derivation. As regards sentential logic, this conception will be extended in so far as not only formulas but also rules may serve as assumptions which can be discharged.
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Natural Deduction Bottom Up [PDF]
Journal of Logic, Language and Information, 2021 AbstractThe paper introduces a new type of rules into Natural Deduction, elimination rules by composition. Elimination rules by composition replace usual elimination rules in the style of disjunction elimination and give a more direct treatment of additive disjunction, multiplicative conjunction, existence quantifier and possibility modality ...
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Hybrid Deduction–Refutation Systems
Axioms, 2019 Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining
Valentin Goranko
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Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory Modulo [PDF]
Logical Methods in Computer Science, 2011 In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied.
Guillaume Burel
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Parsing as natural deduction [PDF]
Proceedings of the 27th annual meeting on Association for Computational Linguistics -, 1989 The logic behind parsers for categorial grammars can be formalized in several different ways. Lambek Calculus (LC) constitutes an example for a natural deduction1 style parsing method.In natural language processing, the task of a parser usually consists in finding derivations for all different readings of a sentence.
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