相关论文: Normalization by gluing for free {\lambda}-theorie…

The theory of associative $n$-categories has recently been proposed as a strictly associative and unital approach to higher category theory. As a foundation for a proof assistant, this is potentially attractive, since it has the potential…

Semantic clusters of a domain form an important feature that can be useful for performing syntactic and semantic disambiguation. Several attempts have been made to extract the semantic clusters of a domain by probabilistic or taxonomic…

Numerous models for grounded language understanding have been recently proposed, including (i) generic models that can be easily adapted to any given task and (ii) intuitively appealing modular models that require background knowledge to be…

Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we…

We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…

We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…

Our research is part of a wider project that aims to investigate and reason about the correctness of scheme-based source code transformations of Erlang programs. In order to formally reason about the definition of a programming language and…

This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…

Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes are corrected. Such learning from positive evidence has been viewed as raising logical…

Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…

It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…

A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…

Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global…

The symbol grounding problem asks how tokens like cat can be about cats, as opposed to mere shapes manipulated in a calculus. We recast grounding from a binary judgment into an audit across desiderata, each indexed by an evaluation tuple…

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…

We show normalisation and decidability of convertibility for a type theory with a hierarchy of universes and a proof irrelevant type of propositions, close to the type system used in the proof assistant Lean. Contrary to previous arguments,…

I show that propositional intuitionistic logic is complete with respect to an adaptation of Dummett's pragmatist justification procedure. In particular, given a pragmatist justification of an argument, I show how to obtain a natural…

This article examines two approaches to verification, one based on using a logic for expressing properties of a system, and one based on showing the system equivalent to a simpler system that obviously has whatever property is of interest.…

This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to…

We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…