Related papers: Tableaux for the Lambek-Grishin calculus
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Multivariate categorical data are routinely collected in many application areas. As the number of cells in the table grows exponentially with the number of variables, many or even most cells will contain zero observations. This severe…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
The connection between classical model theoretical types (MT-types) and logically-geometrical types (LG-types) introduced by B. Plotkin is considered. It is proved that MT-types of two $n$-tuples in two universal algebras coincide if and…
Large language models (LLMs) exhibit strong semantic understanding, yet struggle when user instructions involve ambiguous or conceptually misaligned terms. We propose the Language Graph Model (LGM) to enhance conceptual clarity by…
Evaluating multimodal large language models (MLLMs) is fundamentally challenged by the absence of structured, interpretable, and theoretically grounded benchmarks; current heuristically-grouped tasks have vague cognitive targets,…
In this note, by integrating ideas concerning terminating tableaux-based procedures in modal logics and finite frame property of intuitionistic modal logic IK, we provide new and simpler decidability proofs for FIK and LIK.
Hybrid logic is a modal logic with additional operators specifying nominals and is highly expressive. For example, there is no formula corresponding to the irreflexivity of Kripke frames in basic modal logic, but there is in hybrid logic.…
Logical Natural Language Generation, i.e., generating textual descriptions that can be logically entailed by a structured table, has been a challenge due to the low fidelity of the generation. \citet{chen2020logic2text} have addressed this…
The hyperedge replacement grammar (HRG) formalism is a natural and well-known generalization of context-free grammars. HRGs inherit a number of properties of context-free grammars, e.g. the pumping lemma. This lemma turns out to be a strong…
This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category-theoretical techniques. We connect such classes of algebras…
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…
Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning…
The Lie algebra gl(lambda) dependent on the complex parameter lambda is a continuous version of the Lie algebra gl(inf) of infinite matrices with only finite number of nonzero entries. The gl(lambda) was first introduced by B.L.Feigin in…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…
The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
We introduce $\infty$-type theories as an $\infty$-categorical generalization of the categorical definition of type theories introduced by the second named author. We establish analogous results to the previous work including the…
The paper describes a parser for Categorial Grammar which provides fully word by word incremental interpretation. The parser does not require fragments of sentences to form constituents, and thereby avoids problems of spurious ambiguity.…