Related papers: Interactive Learning-Based Realizability for Heyti…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
The notion of Reactive Turing machine (RTM) was proposed as an orthogonal extension of Turing machines with interaction. RTMs are used to define the notion of executable transition system in the same way as Turing machines are used to…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
It is well known that the R, the set of real numbers, is an abstract set, where almost all its elements cannot be described in any finite language. We investigate possible approaches to what might be called an epi-constructionist approach…
Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…
Existing reasoning evaluation paradigms suffer from different limitations: fixed benchmarks are increasingly saturated and vulnerable to contamination, while preference-based evaluations rely on subjective judgments. We argue that a core…
The field of implicit complexity has recently produced several bounded-complexity programming languages. This kind of language allows to implement exactly the functions belonging to a certain complexity class. We here present a…
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$.…
Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal…
We present a novel approach for recommending actionable strategies by integrating strategic frameworks with decision heuristics through semantic analysis. While strategy frameworks provide systematic models for assessment and planning, and…
Reinforcement learning agents deployed in the real world often have to cope with partially observable environments. Therefore, most agents employ memory mechanisms to approximate the state of the environment. Recently, there have been…
In this paper, we present an interactive semantics for derivations in an infinitary extension of classical logic. The formulas of our language are possibly infinitary trees labeled by propositional variables and logical connectives. We show…
Interactive Machine Learning (IML) shall enable intelligent systems to interactively learn from their end-users, and is quickly becoming more and more important. Although it puts the human in the loop, interactions are mostly performed via…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…
Hierarchical Reinforcement Learning algorithms have successfully been applied to temporal credit assignment problems with sparse reward signals. However, state-of-the-art algorithms require manual specification of sub-task structures, a…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…