Related papers: Hyperformalism for Bunched Natural Deduction Syste…

We study succinctness as a measure of the expressive power of transformers. Succinctness -- how compactly a formalism can describe a language relative to other formalisms -- is a classical notion in logic and automata theory. We prove that…

We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…

Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…

We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension,…

Abductive reasoning, reasoning for inferring explanations for observations, is often mentioned in scientific, design-related and artistic contexts, but its understanding varies across these domains. This paper reviews how abductive…

In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…

Computational properties of networks that can undergo cascades are examined. It is shown that universal Boolean logic circuits can be computed by a global cascade having antagonistic interactions. Determinism and cascade frequency of this…

We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…

We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as…

We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to integral approximation). The…

We show that an interesting class of feed-forward neural networks can be understood as quantitative argumentation frameworks. This connection creates a bridge between research in Formal Argumentation and Machine Learning. We generalize the…

Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…

Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be…

In this note, we provide complexity characterizations of model checking multi-pushdown systems. Multi-pushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard…

We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…