Related papers: Linear Logic by Levels and Bounded Time Complexity
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
Advanced reasoning typically requires Chain-of-Thought prompting, which is accurate but incurs prohibitive latency and substantial test-time inference costs. The standard alternative, fine-tuning smaller models, often sacrifices…
We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate…
Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…
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 rooted in proof theory…
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…
In a previous work we introduced Dual Light Affine Logic (DLAL) ([BaillotTerui04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can be evaluated in polynomial…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
We present a heuristic based algorithm to induce \textit{nonmonotonic} logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important…
We present a new asynchronous model of computation named Stellar Resolution based on first-order unification. This model of computation is obtained as a formalisation of Girard's transcendental syntax programme, sketched in a series of…
We present the stellar resolution, a "flexible" tile system based on Robinson's first-order resolution. After establishing formal definitions and basic properties of the stellar resolution, we show its Turing-completeness and to illustrate…
We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e.…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
The two Girard translations provide two different means of obtaining embeddings of Intuitionistic Logic into Linear Logic, corresponding to different lambda-calculus calling mechanisms. The translations, mapping A -> B respectively to !A -o…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
One of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation…