Related papers: Relational semantics of linear logic and higher-or…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Search in e-Commerce is powered at the core by a structured representation of the inventory, often formulated as a category taxonomy. An important capability in e-Commerce with hierarchical taxonomies is to select a set of relevant leaf…
Iterative refinement has emerged as an effective paradigm for enhancing the capabilities of large language models (LLMs) on complex tasks. However, existing approaches typically implement iterative refinement at the application or prompting…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
Argumentation frameworks ($AF$s) have been extensively developed, but existing higher-order bipolar $AF$s suffer from critical limitations: attackers and supporters are restricted to arguments, multi-valued and fuzzy semantics lack unified…
Proving linearizability of concurrent data structures remains a key challenge for verification. We present temporal interpolation as a new proof principle to conduct such proofs using hindsight arguments within concurrent separation logic.…
We propose a new end-to-end model that treats AMR parsing as a series of dual decisions on the input sequence and the incrementally constructed graph. At each time step, our model performs multiple rounds of attention, reasoning, and…
Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational…
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
Current end-to-end semantic role labeling is mostly accomplished via graph-based neural models. However, these all are first-order models, where each decision for detecting any predicate-argument pair is made in isolation with local…
We present a new approach to automated reasoning about higher-order programs by extending symbolic execution to use behavioral contracts as symbolic values, enabling symbolic approximation of higher-order behavior. Our approach is based on…
The two major systems of formal verification are model checking and algebraic model-based testing. Model checking is based on some form of temporal logic such as linear temporal logic (LTL) or computation tree logic (CTL). One powerful and…
Model Checking is widely applied in verifying the correctness of complex and concurrent systems against a specification. Pure symbolic approaches while popular, suffer from the state space explosion problem due to cross product operations…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
The meaning of a sentence is a function of the relations that hold between its words. We instantiate this relational view of semantics in a series of neural models based on variants of relation networks (RNs) which represent a set of…
Ong has shown that the modal mu-calculus model checking problem (equivalently, the alternating parity tree automaton (APT) acceptance problem) of possibly-infinite ranked trees generated by order-n recursion schemes is n-EXPTIME complete.…
Chain-of-Thought (CoT) prompting has achieved remarkable success in unlocking the reasoning capabilities of Large Language Models (LLMs). Although CoT prompting enhances reasoning, its verbosity imposes substantial computational overhead.…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
Vector space methods that measure semantic similarity and relatedness often rely on distributional information such as co--occurrence frequencies or statistical measures of association to weight the importance of particular co--occurrences.…