Related papers: Restricted Interpolation and Lack Thereof in Stit …
Neural reasoning accuracy improves when generating intermediate reasoning steps. However, the source of this improvement is yet unclear. Here, we investigate and factorize the benefit of generating intermediate steps for symbolic reasoning.…
The ability to extrapolate, i.e., to make predictions on sequences that are longer than those presented as training examples, is a challenging problem for current deep learning models. Recent work shows that this limitation persists in…
Coalition Logic is an important logic in logical studies of strategic reasoning, whose models are concurrent game models. In this paper, first, we systematically discuss three assumptions of concurrent game models and argue that they are…
The notion of Craig interpolant, used as a form of explanation in automated reasoning, is adapted from logical inference to statistical inference and used to explain inferences made by neural networks. The method produces explanations that…
We propose a notion of alternating bisimulation for strategic abilities under imperfect information. The bisimulation preserves formulas of ATL$^*$ for both the {\em objective} and {\em subjective} variants of the state-based semantics with…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis.
While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
The variable inclusion companions of logics have lately been thoroughly studied by multiple authors. There are broadly two types of these companions: the left and the right variable inclusion companions. Another type of companions of logics…
Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…
We present a logic that extends CTL (Computation Tree Logic) with operators that express synchronization properties. A property is synchronized in a system if it holds in all paths of a certain length. The new logic is obtained by using the…
In this paper we present a novel method to overcome membrane locking of thin shells. An interpolation operator into the so-called Regge finite element space is inserted in the membrane energy term to weaken the implicitly given kernel…
Interpolation-based techniques have become popularized in recent years because of their inherently modular and local reasoning, which can scale up existing formal verification techniques like theorem proving, model-checking, abstraction…
ATL is a temporal logic geared towards the specification and verification of properties in multi-agents systems. It allows to reason on the existence of strategies for coalitions of agents in order to enforce a given property. In this…
An unaddressed challenge in multi-agent coordination is to enable AI agents to exploit the semantic relationships between the features of actions and the features of observations. Humans take advantage of these relationships in highly…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…
Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic…
We develop a method to recognize admissibility of $\Pi_{2}$-rules, relating this problem to a specific instance of the unification problem with linear constants restriction, called here "unification with simple variable restriction". It is…