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Starting with Hoare Logic over 50 years ago, numerous program logics have been devised to reason about the diverse programs encountered in the real world. This includes reasoning about computational effects, particularly those effects that…
The recent notion of graded modal types provides a framework for extending type theories with fine-grained data-flow reasoning. The Granule language explores this idea in the context of linear types. In this practical setting, we observe…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path…
Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…
Separation Logic is an effective Program Logic for proving programs that involve pointers. Reasoning with pointers becomes difficult especially when there is aliasing arising due to several pointers to a given cell location. In this paper,…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
Recently, research has increasingly focused on developing efficient neural network architectures. In this work, we explore logic gate networks for machine learning tasks by learning combinations of logic gates. These networks comprise logic…
Linear logic is a substructural logic proposed as a refinement of classical and intuitionistic logics, with applications in programming languages, game semantics, and quantum physics. We present a template for Gentzen-style linear logic…
A distributed logic programming language with support for meta-programming and stream processing offers a variety of interesting research problems, such as: How can a versatile and stable data structure for the indexing of a large number of…
Pre-trained large language models (LMs) struggle to perform logical reasoning reliably despite advances in scale and compositionality. In this work, we tackle this challenge through the lens of symbolic programming. We propose DSR-LM, a…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…