Related papers: On expressive power and class invariance
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
Deep models that are both effective and explainable are desirable in many settings; prior explainable models have been unimodal, offering either image-based visualization of attention weights or text-based generation of post-hoc…
This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional "names". We make three contributions. First, we study its model theory, providing adequate notions…
The paper investigates behavioural equivalence between programs in a call-by-value functional language extended with a signature of (algebraic) effect-triggering operations. Two programs are considered as being behaviourally equivalent if…
Similar to modal connectives, the exponential ! in intuitionistic linear logic (ILL) is not canonical, in the sense that if $i\not= j$ then $!^i F\not\equiv !^j F$. Intuitively, this means that we can mark the exponential with labels taken…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Several queries and scores have recently been proposed to explain individual predictions over ML models. Given the need for flexible, reliable, and easy-to-apply interpretability methods for ML models, we foresee the need for developing…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
Compositionality is considered central to language abilities. As performant language systems, how do large language models (LLMs) do on compositional tasks? We evaluate adjective-noun compositionality in LLMs using two complementary setups:…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
Researchers are using deep learning models to explore the emergence of language in various language games, where agents interact and develop an emergent language to solve tasks. We focus on the factors that determine the expressivity of…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
(Maher 2012) introduced an approach for relative expressiveness of defeasible logics, and two notions of relative expressiveness were investigated. Using the first of these definitions of relative expressiveness, we show that all the…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…