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Restricted non-deterministic matrices (RNmatrices) impose constraints on the rows of non-deterministic matrices (Nmatrices), filtering out "unsound" rows and retaining only "valid" ones. This yields a more expressive framework than standard…
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
Coherent discourse is distinguished from a mere collection of utterances by the satisfaction of a diverse set of constraints, for example choice of expression, logical relation between denoted events, and implicit compatibility with…
We consider existential rules (aka Datalog+) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these…
In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus uses labels and transition formulas and can be used to prove decidability and space…
Interaction nets are a form of restricted graph rewrite system that can serve as a graphical or textual programming language. As such, benefits include one-step confluence, ease of parallelism and explicit garbage collection. However, some…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
Applying new computing paradigms like quantum computing to the field of machine learning has recently gained attention. However, as high-dimensional real-world applications are not yet feasible to be solved using purely quantum hardware,…
Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form $\forall x.A$ (for quantifier-free $A$) to a method…
Deploying generative machine learning techniques to generate novel chemical structures based on molecular fingerprint representation has been well established in molecular design. Typically, sequential learning (SL) schemes such as hidden…
This paper investigates the extension of lattice-based logics into modal languages. We observe that such extensions admit multiple approaches, as the interpretation of the necessity operator is not uniquely determined by the underlying…
Answering compositional questions that require multiple steps of reasoning against text is challenging, especially when they involve discrete, symbolic operations. Neural module networks (NMNs) learn to parse such questions as executable…
Text-speech joint spoken language modeling (SLM) aims at natural and intelligent speech-based interactions, but developing such a system may suffer from modality mismatch: speech unit sequences are much longer than text tokens. Prior work…
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…
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…
We explore an inquisitive modal logic designed to reason about neighborhood models. This logic is based on an inquisitive strict conditional operator, which quantifies over neighborhoods, and which can be applied to both statements and…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
Modal analysis based on the quasi-normal modes (QNM), also called resonant states, has emerged as a promising way for modeling the resonant interaction of light with open optical cavities. However, the fields associated with QNM in open…
We introduce a variant of modal logic, dubbed EXISTENTIAL COUNTING MODAL LOGIC (ECML), which captures a vast majority of problems known to be tractable in single exponential time when parameterized by treewidth. It appears that all these…