Related papers: On Constraint-Based Lambek Calculi
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
There is an increased interest in solving complex constrained problems where part of the input is not given as facts but received as raw sensor data such as images or speech. We will use "visual sudoku" as a prototype problem, where the…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
In this project, a rather complete proof-theoretical formalization of Lambek Calculus (non-associative with arbitrary extensions) has been ported from Coq proof assistent to HOL4 theorem prover, with some improvements and new theorems.…
The mixing set with a knapsack constraint arises as a substructure in mixed-integer programming reformulations of chance-constrained programs with stochastic right-hand-sides over a finite discrete distribution. Recently, Luedtke et al.…
We introduce a comprehensive Linguistic Benchmark designed to evaluate the limitations of Large Language Models (LLMs) in domains such as logical reasoning, spatial intelligence, and linguistic understanding, among others. Through a series…
Despite their success in various domains, the growing dependence on GNNs raises a critical concern about the nature of the combinatorial reasoning underlying their predictions, which is often hidden within their black-box architectures.…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
Convertibility checking - determining whether two lambda-terms are equal up to reductions - is a crucial component of proof assistants and dependently-typed languages. Practical implementations often use heuristics to quickly conclude that…
We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
The linguistic applications of the Lambek calculus suggest its semantics over algebras of formal languages. A straightforward approach to construct such semantics indeed yields a brilliant completeness theorem (Pentus 1995). However,…
The molecular computing has been successfully employed to solve more and more complex computation problems. However, as an important complex problem, the model checking are still far from fully resolved under the circumstance of molecular…