Logic Linguist is a specialized tool designed to assist in the translation of natural language statements into first-order logic. This process is foundational for applications in formal logic, computational linguistics, and artificial intelligence, where precise, unambiguous representations of statements are required.
Using the symbolization key from Exercise \(4.2.5\), translate each English-language assertion into First-Order Logic. If there is a dog larger than Fergis, then there is a dog larger than Emerson. Every dog is larger than some dog. There is an animal that is smaller than every dog.
Translating natural language sentences to first-order logic (NL-FOL translation) is a longstanding challenge in the NLP and formal logic literature. This paper introduces LogicLLaMA, a LLaMA-7B model fine-tuned for NL-FOL translation using LoRA on a single GPU. LogicLLaMA is capable of directly translating natural language into FOL rules, which outperforms GPT-3.5. LogicLLaMA is also equipped ...
Key take-aways from the translation examples above: Note that changing the order of our quantifiers produces drastically different meanings in these statements. Note that because of operator precedence, the major connective for the universal quantifier in the second FOL example above is implication ($\rightarrow$), not conjunction ($\wedge$).
LogicLLaMA: A language model that translates natural-language (NL) statements into first-order logic (FOL) rules. It is trained by fine-tuning the LLaMA-7B model on the MALLS dataset.. MALLS (large language Model generAted natural-Language-to-first-order-Logic pairS): a dataset consists of 34K pairs of real-world natural language (NL) statements and the corresponding first-order logic (FOL ...
Guide to First-Order Logic Translations.WHY do we use Implication with universal quantifier ?WHY do we use Conjunction with existential quantifier ?Learn the...
Almost directly copied from Peter Suber's Translation Tips. Propositional Logic; 1st Order Logic. Singly General Monadic; Multiply General Monadic; Polyadic. In this hand-out I treat the notation of truth-functional propositional logic and first-order predicate logic as a language, and give guidance on translating from English into this foreign language.
Example 1 for basics. This is a really trivial example. We will give two facts: john is a father of pete and pete is a father of mark.We will ask whether from these two facts we can derive that john is a father of pete: obviously we can.. The facts and the question are written in predicate logic, with the question posed as a negation, from which gkc derives contradiction.
Translation into FOL Sentences. Let S(x) mean x is a skier, M(x) mean x is a mountain climber, and L(x,y) mean x likes y, where the domain of the first variable is Hoofers Club members, and the domain of the second variable is snow and rain. We can now translate the above English sentences into the following FOL wffs: (Ax) S(x) v M(x) ~(Ex) M(x ...
It is also possible to convert natural language into first-order logic using a discourse representation theory. For example, the ACE reasoner is an automated theorem prover that can convert English text into first-order logical predicates.
First-order logic is a powerful logical system for reasoning about groups of objects and their properties. It is also how, later in the quarter, we'll formally define the terms we're working with. This lecture introduces the syntax of first-order logic, explains how it works, and goes over the basics of how to translate into first-order logic.
many first-order logic translations. It is worth committing these patterns to memory. We’ll be using them throughout the day and they form the backbone of many first-order logic translations. The Art of Translation. Using the predicates - Person(p), which states that p is a person, and
first-order-logic; logic-translation; See similar questions with these tags. Featured on Meta Changes to reporting for the [status-review] escalation process. Chat link being added to left navigation bar. Related. 0. Translate from English to first-order logic. 1. ...
Syntax of first order formulas First order languages. A first order language is a language characterized by: A set of constant symbols; A set of variable symbols; A set of function symbols, each with an associated arity; A set of predicate symbols, each with an associated arity; The logic symbols ¬, ∧, ∨, →, ←, ↔; The quantifier ...
Working through first order logic examples and want to make sure I am translating correctly before moving on to harder resolution of first order logic. Use the predicates HasBugs(x), Comments(x), HighQuality(x), QuickSolve(x), and BestPractice(x), where x is a programmer. My translations are: #1
10/6 First-Order Logic, Part II 6. 10/9 Functions, Part I 7. 10/11 Functions, Part II 8. 10/13 Set Theory Revisited 9. 10/16 Graphs, Part I 10. 10/18 ... This animated guide explains how to translate English statements into first-order logic. Link. Guide to Logic Translations.
Similarly to \(\phi\mapsto\phi^*\) there is also a translation from the many-sorted logic into second-order logic. 13. The proof is just as the proof given by Henkin for the Completeness Theorem of first order logic. Suppose we have a countable theory which is consistent in the sense that no contradiction can be derived. We add new constant ...
