Related papers: Rank logic is dead, long live rank logic!
Recent reasoning-focused language models achieve high accuracy by generating lengthy intermediate reasoning paths before producing final answers. While this approach is effective in solving problems that require logical thinking, long…
We study two extensions of FO2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, "the letter $a$ appears between…
Our primary motivation is the comparison of two different traditions used in ICC to characterize the class FPTIME of the polynomial time computable functions. On one side, FPTIME can be captured by Intuitionistic Light Affine Logic (ILAL),…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
Arithmetic complexity is considered simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic…
Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential.…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
Reasoning has emerged as the next major frontier for language models (LMs), with rapid advances from both academic and industrial labs. However, this progress often outpaces methodological rigor, with many evaluations relying on…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
Preference-based Reinforcement Learning (PbRL) replaces reward values in traditional reinforcement learning by preferences to better elicit human opinion on the target objective, especially when numerical reward values are hard to design or…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes…
Ranking documents using Large Language Models (LLMs) by directly feeding the query and candidate documents into the prompt is an interesting and practical problem. However, researchers have found it difficult to outperform fine-tuned…
The components underpinning PLMs -- large weight matrices -- were shown to bear considerable redundancy. Matrix factorization, a well-established technique from matrix theory, has been utilized to reduce the number of parameters in PLM.…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive…
Semiring provenance is a successful approach to provide detailed information on the combinations of atomic facts that are responsible for the result of a query. In particular, interpretations in general provenance semirings of polynomials…