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In some optimal control problems, complex relationships between states and inputs cannot be easily represented using continuous constraints, necessitating the use of discrete logic instead. This paper presents a method for incorporating…
The prevailing approach to distilling reasoning from Large Language Models (LLMs)-behavioral cloning from textual rationales-is fundamentally limited. It teaches Small Language Models (SLMs) to mimic surface-level patterns rather than the…
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…
This paper introduces STRASS: Summarization by TRAnsformation Selection and Scoring. It is an extractive text summarization method which leverages the semantic information in existing sentence embedding spaces. Our method creates an…
Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
A linear constraint system is specified by linear equations over the group $\ZZ_d$ of integers modulo $d$. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is…
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…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by translating logical rules directly into equations. The former type…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…