Three Dogmas, a Puzzle and its Solution

• URL: http://arxiv.org/abs/2310.19123v1
• Date: Sun, 29 Oct 2023 19:20:38 GMT
• Title: Three Dogmas, a Puzzle and its Solution
• Authors: Elnaserledinellah Mahmood Abdelwahab
• Abstract summary: In this paper we show that those assumptions contradict basic principles of Arabic. The Logicians ideas, that within Natural Language words refer to objects, 'ToBe'-constructions represent identity statements. Indefinite Descriptions must be replaced by existential quantifiers to form meaningful Sentences and Symbols can have no interpretation-independent meanings.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modern Logics, as formulated notably by Frege, Russell and Tarski involved basic assumptions about Natural Languages in general and Indo-European Languages in particular, which are contested by Linguists. Based upon those assumptions, formal Languages were designed to overcome what Logicians claimed to be 'defects' of Natural Language. In this paper we show that those assumptions contradict basic principles of Arabic. More specifically: The Logicians ideas, that within Natural Language words refer to objects, 'ToBe'-constructions represent identity statements, Indefinite Descriptions must be replaced by existential quantifiers to form meaningful Sentences and Symbols can have no interpretation-independent meanings, are all falsified using undisputed principles of Arabic. The here presented falsification serves two purposes. First, it is used as a factual basis for the rejection of approaches adopting Semantic axioms of Mathematical Logics as Models for meaning of Arabic Syntax. Second, it shows a way to approach the important computational problem: Satisfiability (SAT). The described way is based upon the realization that parsing Arabic utilizes the existence of 'meaning-particles' within Syntax to efficiently recognize words, phrases and Sentences. Similar meaning-particles are shown to exist in 3CNF formulas, which, when properly handled within the machinery of 3SAT-Solvers, enable structural conditions to be imposed on formulas, sufficient alone to guarantee the efficient production of non-exponentially sized Free Binary Decision Diagrams (FBDDs). We show, why known exponential Lower Bounds on sizes of FBDDs do not contradict our results and reveal practical evidence, obtained for multiplication circuits, supporting our claims.

Related papers

• LogicSkills: A Structured Benchmark for Formal Reasoning in Large Language Models [37.930280449304696]
  We isolate three fundamental logic skills into first-order logic models.<n>Items are drawn from two first-order logic (without English) and are presented in both a and a Carroll-style nonce words.<n>Across leading models, performance is substantially lower but high validity.
  arXiv  Detail & Related papers  (2026-02-06T09:38:44Z)
• Are Language Models Efficient Reasoners? A Perspective from Logic Programming [109.47572890883248]
  Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of human-like reasoning: efficiency.<n>We propose a framework for assessing LM reasoning efficiency through the lens of logic programming.
  arXiv  Detail & Related papers  (2025-10-29T15:30:31Z)
• Reasoning is about giving reasons [55.56111618153049]
  We show that we can identify and extract the logical structure of natural language arguments in three popular reasoning datasets with high accuracies.<n>Our approach supports all forms of reasoning that depend on the logical structure of the natural language argument.
  arXiv  Detail & Related papers  (2025-08-20T07:26:53Z)
• Interleaving Logic and Counting [5.71869130799784]
  Reasoning with quantifier expressions in natural language combines logical and arithmetical features.<n>Our topic is this cooperation of styles as it occurs in common linguistic usage.
  arXiv  Detail & Related papers  (2025-07-07T17:30:29Z)
• Under the Shadow of Babel: How Language Shapes Reasoning in LLMs [27.48119976373105]
  We show that large language models internalize the habitual logical structures embedded in different languages.<n>Our study reveals three key findings: (1) LLMs exhibit typologically aligned attention patterns, focusing more on causes and sentence-initial connectives in Chinese, while showing a more balanced distribution in English.
  arXiv  Detail & Related papers  (2025-06-19T09:06:38Z)
• Learning to Reason via Mixture-of-Thought for Logical Reasoning [56.24256916896427]
  Mixture-of-Thought (MoT) is a framework that enables LLMs to reason across three complementary modalities: natural language, code, and truth-table.<n>MoT adopts a two-phase design: (1) self-evolving MoT training, which jointly learns from filtered, self-generated rationales across modalities; and (2) MoT inference, which fully leverages the synergy of three modalities to produce better predictions.
  arXiv  Detail & Related papers  (2025-05-21T17:59:54Z)
• Fundamental Principles of Linguistic Structure are Not Represented by o3 [3.335047764053173]
  o3 model fails to generalize basic phrase structure rules. It fails to correctly rate and explain acceptability dynamics. It fails to distinguish between instructions to generate unacceptable semantic vs. unacceptable syntactic outputs.
  arXiv  Detail & Related papers  (2025-02-15T23:53:31Z)
• TabVer: Tabular Fact Verification with Natural Logic [11.002475880349452]
  We propose a set-theoretic interpretation of numerals and arithmetic functions in the context of natural logic. We leverage large language models to generate arithmetic expressions by generating questions about salient parts of a claim which are answered by executing functions on tables. In a few-shot setting on FEVEROUS, we achieve an accuracy of 71.4, outperforming both fully neural and symbolic reasoning models by 3.4 points.
  arXiv  Detail & Related papers  (2024-11-02T00:36:34Z)
• Scaling Synthetic Logical Reasoning Datasets with Context-Sensitive Declarative Grammars [0.6537995248511139]
  We present a declarative framework with flexible context-sensitive rules binding multiple languages. We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks.
  arXiv  Detail & Related papers  (2024-06-16T18:10:49Z)
• LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models [52.03659714625452]
  Recently developed large language models (LLMs) have been shown to perform remarkably well on a wide range of language understanding tasks. But, can they really "reason" over the natural language? This question has been receiving significant research attention and many reasoning skills such as commonsense, numerical, and qualitative have been studied.
  arXiv  Detail & Related papers  (2024-04-23T21:08:49Z)
• Language Models can be Logical Solvers [99.40649402395725]
  We introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers.
  arXiv  Detail & Related papers  (2023-11-10T16:23:50Z)
• LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers [60.009969929857704]
  Logical reasoning is an important task for artificial intelligence with potential impacts on science, mathematics, and society. In this work, we reformulating such tasks as modular neurosymbolic programming, which we call LINC. We observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate.
  arXiv  Detail & Related papers  (2023-10-23T17:58:40Z)
• Enhancing Zero-Shot Chain-of-Thought Reasoning in Large Language Models through Logic [19.476840373850653]
  Large language models show hallucinations as their reasoning procedures are unconstrained by logical principles. We propose LoT (Logical Thoughts), a self-improvement prompting framework that leverages principles rooted in symbolic logic. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of enhanced reasoning by logic.
  arXiv  Detail & Related papers  (2023-09-23T11:21:12Z)
• Language Models as Inductive Reasoners [125.99461874008703]
  We propose a new paradigm (task) for inductive reasoning, which is to induce natural language rules from natural language facts. We create a dataset termed DEER containing 1.2k rule-fact pairs for the task, where rules and facts are written in natural language. We provide the first and comprehensive analysis of how well pretrained language models can induce natural language rules from natural language facts.
  arXiv  Detail & Related papers  (2022-12-21T11:12:14Z)
• APOLLO: A Simple Approach for Adaptive Pretraining of Language Models for Logical Reasoning [73.3035118224719]
  We propose APOLLO, an adaptively pretrained language model that has improved logical reasoning abilities. APOLLO performs comparably on ReClor and outperforms baselines on LogiQA.
  arXiv  Detail & Related papers  (2022-12-19T07:40:02Z)
• Formal Specifications from Natural Language [3.1806743741013657]
  We study the ability of language models to translate natural language into formal specifications with complex semantics. In particular, we fine-tune off-the-shelf language models on three datasets consisting of structured English sentences.
  arXiv  Detail & Related papers  (2022-06-04T10:49:30Z)
• Quantification and Aggregation over Concepts of the Ontology [0.0]
  We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We present an extension of first-order logic to support such abstractions, and show that it allows writing expressions of knowledge that are elaboration tolerant.
  arXiv  Detail & Related papers  (2022-02-02T07:49:23Z)
• Learning Symbolic Rules for Reasoning in Quasi-Natural Language [74.96601852906328]
  We build a rule-based system that can reason with natural language input but without the manual construction of rules. We propose MetaQNL, a "Quasi-Natural" language that can express both formal logic and natural language sentences. Our approach achieves state-of-the-art accuracy on multiple reasoning benchmarks.
  arXiv  Detail & Related papers  (2021-11-23T17:49:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.