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DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…

Inductive Logic Programming (ILP) combines rule-based and statistical artificial intelligence methods, by learning a hypothesis comprising a set of rules given background knowledge and constraints for the search space. We focus on extending…

A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL)…

Heterogeneous information networks (HIN) have gained increasing popularity in recent years for capturing complex relations between diverse types of nodes. Meta-structures are proposed as a useful tool to identify the important patterns in…

Hybrid systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. Legged locomotion, robotic manipulation, and additive manufacturing are representative examples…

Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau…

For over two decades Separation Logic has been arguably the most popular framework for reasoning about heap-manipulating programs, as well as reasoning about shared resources and permissions. Separation Logic is often extended to include…

We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…

The integration of Deep Learning (DL) in System Dynamics (SD) modeling for transportation logistics offers significant advantages in scalability and predictive accuracy. However, these gains are often offset by the loss of explainability…

Large Language Models (LLMs) increasingly rely on Chain-of-Thought (CoT) reasoning to improve accuracy on complex tasks. However, always generating lengthy reasoning traces is inefficient, leading to excessive token usage and higher…

Decision-making under changing conditions remains a fundamental challenge in many real-world systems. Existing approaches often fail to generalize across shifting regimes and exhibit unstable behavior under uncertainty. This raises the…

This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…

Choreographic programming is a paradigm where a concurrent or distributed system is developed in a top-down fashion. Programs, called choreographies, detail the desired interactions between processes, and can be compiled to distributed…

PDDL+ planning has its semantics rooted in hybrid automata (HA) and recent work has shown that it can be modeled as a network of HAs. Addressing the complexity of nonlinear PDDL+ planning as HAs requires both space and time efficient…

The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to…

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…

Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) by generating natural language (NL) rationales that lead to the final answer. However, it struggles with numerical…

In-context learning (ICL) enables large language models (LLMs) to perform downstream tasks through advanced prompting and high-quality demonstrations. However, traditional ICL paradigms encounter significant limitations in complex reasoning…