相关论文: Three Dogmas, a Puzzle and its Solution
Large Language Models (LLMs) have impressive capabilities, but are prone to outputting falsehoods. Recent work has developed techniques for inferring whether a LLM is telling the truth by training probes on the LLM's internal activations.…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
We present a procedure which allows us to recover classical and nonclassical logical structures as \emph{concrete logics} associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for…
Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…
We compare three satisfiability notions for propositional formulas in the language {not, and, or} over a fixed finite-dimensional Hilbert space H=F^d with F in {R, C}. The first is the standard Hilbert-lattice semantics on the subspace…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Much of philosophical logic and all of philosophy of language make empirical claims about the vernacular natural language. They presume semantics under which `and' and `or' are related by the dually paired distributive and absorption laws.…
It follows from the famous Fagin's theorem that all problems in NP are expressible in existential second-order logic (ESO), and vice versa. Indeed, there are well-known ESO characterizations of NP-complete problems such as 3-colorability,…
Semantic degeneracy represents a fundamental property of natural language that extends beyond simple polysemy to encompass the combinatorial explosion of potential interpretations that emerges as semantic expressions increase in complexity.…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
The term natural language refers to any system of symbolic communication (spoken, signed or written) without intentional human planning and design. This distinguishes natural languages such as Arabic and Japanese from artificially…
In recent years, large language models (LLMs) have demonstrated significant success in performing varied natural language tasks such as language translation, question-answering, summarizing, fact-checking, etc. Despite LLMs' impressive…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
Large language models (LLMs) face significant challenges when processing complex rule systems, as they typically treat interdependent rules as unstructured textual data rather than as logically organized frameworks. This limitation results…
Natural language numbers are an example of compositional structures, where larger numbers are composed of operations on smaller numbers. Given that compositional reasoning is a key to natural language understanding, we propose novel…
Our goal is to answer elementary-level science questions using knowledge extracted automatically from science textbooks, expressed in a subset of first-order logic. Given the incomplete and noisy nature of these automatically extracted…
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
NLP tasks differ in the semantic information they require, and at this time no single se- mantic representation fulfills all requirements. Logic-based representations characterize sentence structure, but do not capture the graded aspect of…