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Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…

This paper illustrates how a Prolog program, using chronological backtracking to find a solution in some search space, can be enhanced to perform intelligent backtracking. The enhancement crucially relies on the impurity of Prolog that…

Decision trees are prized for their interpretability and strong performance on tabular data. Yet, their reliance on simple axis-aligned linear splits often forces deep, complex structures to capture non-linear feature effects, undermining…

We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization…

Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and non-termination are undecidable problems in Turing-complete languages. However, some declarative languages offer a…

In this paper, general logic-systems are investigated. It is shown that there are infinitely many finite consequence operators defined on a fixed language L that cannot be generated from a finite logic-system. It is shown that a set map is…

An equational logic program is a set of directed equations or rules, which are used to compute in the obvious way (by replacing equals with ``simpler'' equals). We present static analysis techniques for efficient equational logic…

Recent advances in large reasoning language models (LRLMs) rely on test-time scaling, which extends long chain-of-thought (CoT) generation to solve complex tasks. However, overthinking in long CoT not only slows down the efficiency of…

Code analysis is fundamental in Software Engineering, supporting debugging, optimization, and security assessment. Human developers approach it through syntax parsing, static semantics inference, and dynamic reasoning. Traditional tools are…

Grounded theory offers deep insights from qualitative data, but its reliance on expert-intensive manual coding presents a major scalability bottleneck. Existing computational tools either fail on full automation or lack flexible schema…

Meta continual learning algorithms seek to train a model when faced with similar tasks observed in a sequential manner. Despite promising methodological advancements, there is a lack of theoretical frameworks that enable analysis of…

We investigate nonlinear prediction in an online setting and introduce a hybrid model that effectively mitigates, via an end-to-end architecture, the need for hand-designed features and manual model selection issues of conventional…

Compositional generalization is a basic mechanism in human language learning, which current neural networks struggle with. A recently proposed Disentangled sequence-to-sequence model (Dangle) shows promising generalization capability by…

Dynamic graphs serve as a generic abstraction and description of the evolutionary behaviors of various complex systems (e.g., social networks and communication networks). Temporal link prediction (TLP) is a classic yet challenging inference…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

We consider the problem of synthesizing programs with numerical constants that optimize a quantitative objective, such as accuracy, over a set of input-output examples. We propose a general framework for optimal synthesis of such programs…

Goal Recognition is the task of discerning the correct intended goal that an agent aims to achieve, given a set of possible goals, a domain model, and a sequence of observations as a sample of the plan being executed in the environment.…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

We study the characterization and computation of general policies for families of problems that share a structure characterized by a common reduction into a single abstract problem. Policies $\mu$ that solve the abstract problem P have been…

This research introduces a new parsing approach, based on earlier syntactic work on context free grammar (CFG) and generalized phrase structure grammar (GPSG). The approach comprises both a new parsing algorithm and a set of syntactic rules…