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Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the…
Businesses, governmental bodies and NGO's have an ever-increasing amount of data at their disposal from which they try to extract valuable information. Often, this needs to be done not only accurately but also within a short time frame.…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
First-order temporal logics are notorious for their bad computational behaviour. It is known that even the two-variable monadic fragment is highly undecidable over various linear timelines, and over branching time even one-variable…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
Integrating heterogeneous data sources and expert knowledge is essential for overcoming data scarcity and enhancing estimation accuracy. Two main frameworks naturally arise to perform the integration of these multiple sources: sequential…
Multimodal alignment is critical for bridging the semantic gap in information retrieval. However, traditional pairwise strategies introduce a geometric blind spot: while they align anchor modalities (e.g., text) with others, they lack…
We introduce derivation depth-a computable metric of the reasoning effort needed to answer a query based on a given set of premises. We model information as a two-layered structure linking abstract knowledge with physical carriers, and…
A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed…
We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…
Knowledge facts are typically represented by relational triples, while we observe that some commonsense facts are represented by the triples whose forms are inconsistent with the expression of language. This inconsistency puts forward a…
A corpus of recent work has revealed that the learned index can improve query performance while reducing the storage overhead. It potentially offers an opportunity to address the spatial query processing challenges caused by the surge in…
Multimodal large language models often struggle with faithful reasoning in complex visual scenes, where intricate entities and relations require precise visual grounding at each step. This reasoning unfaithfulness frequently manifests as…
The trie data structure is a good choice for finite maps whose keys are data structures (trees) rather than atomic values. But what if we want the keys to be patterns, each of which matches many lookup keys? Efficient matching of this kind…
Multilingual language models achieve strong aggregate performance yet often behave unpredictably across languages, scripts, and cultures. We argue that mechanistic explanations for such models should satisfy a \emph{causal} standard: claims…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Spatial reasoning -- the ability to perceive and reason about relationships in space -- advances vision-language models (VLMs) from visual perception toward spatial semantic understanding. Existing approaches either revisit local image…