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Recently machine learning using neural networks (NN) has been developed, and many new methods have been suggested. These methods are optimized for the type of input data and work very effectively, but they cannot be used with any kind of…
We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the…
The expressiveness of propositional non-clausal (NC) formulas is exponentially richer than that of clausal formulas. Yet, clausal efficiency outperforms non-clausal one. Indeed, a major weakness of the latter is that, while Horn clausal…
We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
Active learning of timed languages is concerned with the inference of timed automata from observed timed words. The agent can query for the membership of words in the target language, or propose a candidate model and verify its equivalence…
In natural languages, words are used in association to construct sentences. It is not words in isolation, but the appropriate combination of hierarchical structures that conveys the meaning of the whole sentence. Neural networks can capture…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
The Right to Explanation and the Right to be Forgotten are two important principles outlined to regulate algorithmic decision making and data usage in real-world applications. While the right to explanation allows individuals to request an…
Although large language models demonstrate emergent abilities in solving math word problems, there is a challenging task in complex multi-step mathematical reasoning tasks. To improve model performance on mathematical reasoning tasks,…
Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
Forgetting a specific belief revision episode may not erase information because the other revisions may provide or entail the same information. Whether it does was proved coNP-hard for sequences of two arbitrary lexicographic revisions or…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
Sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time. These logics arise from different choices for various parameters. All the logics considered involve the discrete…
This paper presents a fundamental algorithm for parsing natural language sentences into dependency trees. Unlike phrase-structure (constituency) parsers, this algorithm operates one word at a time, attaching each word as soon as it can be…
Standard deep learning systems require thousands or millions of examples to learn a concept, and cannot integrate new concepts easily. By contrast, humans have an incredible ability to do one-shot or few-shot learning. For instance, from…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
Deterministic 2-head finite automata which are machines that process an input word from both ends are analyzed for their ability to perform reversible computations. This implies that the automata are backward deterministic, enabling unique…
Most program induction approaches require predefined, often hand-engineered, background knowledge (BK). To overcome this limitation, we explore methods to automatically acquire BK through multi-task learning. In this approach, a learner…