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发表于 2025-3-21 19:33:47
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发表于 2025-3-21 23:29:29
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发表于 2025-3-22 04:19:28
https://doi.org/10.1007/978-3-030-64811-4Mathematical Logic and Foundations; Propositional Logic; Predicate Logic; Modal Logic; First-Order Logic
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发表于 2025-3-22 08:26:15
Basic Notions,here is one thing on which most definitions agree, it is that logic deals with the principles of correct reasoning. To explain what this means, we will start with some preliminary clarifications about the terms ‘reasoning’, ‘correct’, and ‘principles’.
售穴
发表于 2025-3-22 09:57:23
The Symbols of Predicate Logic, expressions. .. has a denumerable set of . ., ., .…, which represent singular terms, and a denumerable set of . ., ., .…, which represent predicates. Each predicate letter has . places, for some .. One-place predicate letters represent monadic predicates, that is, predicates that apply to single objects and express properties.
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发表于 2025-3-22 14:35:22
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ODIUM
发表于 2025-3-22 19:10:44
The Symbols of Propositional Logic,This chapter introduces a propositional language called .. The alphabet of . is constituted by three categories of symbols:
的’
发表于 2025-3-22 22:22:49
The Language L,Chapter . introduced the symbols of ., explained their meaning, and illustrated how they can be used to formalize sentences of a natural language. Now it is time to define . in a rigorous way by making fully explicit its syntax and its semantics.
Delectable
发表于 2025-3-23 01:53:18
Logical Consequence in L,As anticipated in Sect. ., there are two ways to characterize a set of valid forms expressible in a language: one is semantic, the other is syntactic.
能量守恒
发表于 2025-3-23 09:15:39
The System ,,This chapter outlines a natural deduction system in . called .. As explained in Sect. ., a natural deduction system is constituted by a set of inference rules that are taken to be intuitively correct. Assuming our definition of validity as necessary truth preservation, this is to say that the rules of . necessarily preserve truth.