Related papers: A Logic for Non-Deterministic Parallel Abstract St…
We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…
ASPIC-style structured argumentation frameworks provide a formal basis for reasoning in artificial intelligence by combining internal argument structure with abstract argumentation semantics. A key challenge in these frameworks is ensuring…
We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach (which has been the…
The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the…
Abstract machines for strong evaluation of the $\lambda$-calculus enter into arguments and have a set of transitions for backtracking out of an evaluated argument. We study a new abstract machine which avoids backtracking by splitting the…
In this paper, we have introduced the deterministic variant of parallel communicating Watson-Crick automata systems. We show that similar to the non-deterministic version, the deterministic version can also recognise some non-regular…
Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. In contrast, human cognition fluidly adapts between intuitive, heuristic (System 1)…
We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…
As a mathematical model of self-assembling systems, Winfree's abstract Tile Assembly Model (aTAM) is a remarkable platform for studying the behaviors and powers of self-assembling systems. Capable of Turing universal computation, the aTAM…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
Analogical reasoning is a fundamental capacity of human cognition that allows us to reason abstractly about novel situations by relating them to past experiences. While it is thought to be essential for robust reasoning in AI systems,…
The problem of completing a large low rank matrix using a subset of revealed entries has received much attention in the last ten years. The main result of this paper gives a necessary and sufficient condition, stated in the language of…
Finite state machines are widely used as a sound mathematical formalism that appropriately describes large scale, distributed and complex systems. Multiple interactions of finite state machines in complex systems are well captured by the…
Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…
Neuro-symbolic reasoning increasingly demands frameworks that unite the formal rigor of logic with the interpretability of large language models (LLMs). We introduce an end to end explainability by construction pipeline integrating the…
Analogical reasoning -- the capacity to identify and map structural relationships between different domains -- is fundamental to human cognition and learning. Recent studies have shown that large language models (LLMs) can sometimes match…
Large language models (LLMs) and theorem provers (TPs) can be effectively combined for verifiable natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…