Related papers: A Two-Watched Literal Scheme for First-Order Logic

In a previous work we introduced Dual Light Affine Logic (DLAL) ([BaillotTerui04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can be evaluated in polynomial…

Deadlocks are a major source of bugs in concurrent programs. They are hard to predict, because they may only occur under specific scheduling conditions. Dynamic analysis attempts to identify potential deadlocks by examining a single…

We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where…

Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

We present a novel approach to efficiently learn a simultaneous translation model with coupled programmer-interpreter policies. First, wepresent an algorithmic oracle to produce oracle READ/WRITE actions for training bilingual…

An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…

Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…

Combining the representations of the words that make up a sentence into a cohesive whole is difficult, since it needs to account for the order of words, and to establish how the words present relate to each other. The solution we propose…

Cyber-security is an important societal concern. Cyber-attacks have increased in numbers as well as in the extent of damage caused in every attack. Large organizations operate a Cyber Security Operation Center (CSOC), which form the first…

We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…

In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic…

This paper studies the challenging continual learning (CL) setting of Class Incremental Learning (CIL). CIL learns a sequence of tasks consisting of disjoint sets of concepts or classes. At any time, a single model is built that can be…

Answering complex queries over incomplete knowledge graphs (KGs) is a challenging job. Most previous works have focused on learning entity/relation embeddings and simulating first-order logic operators with various neural networks. However,…

Foundation models, such as Large language Models (LLMs), have attracted significant amount of interest due to their large number of applications. However, when handling tasks involving repetitive sub-tasks and/or deceptive contents, such as…

Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…

Many tasks in Natural Language Processing involve recognizing lexical entailment. Two different approaches to this problem have been proposed recently that are quite different from each other. The first is an asymmetric similarity measure…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

Long-term action recognition (LTAR) is challenging due to extended temporal spans with complex atomic action correlations and visual confounders. Although vision-language models (VLMs) have shown promise, they often rely on statistical…