Related papers: Step-Indexed Relational Reasoning for Countable No…
We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
We present a novel and well automatable approach to formal verification of C programs with underspecified semantics, i.e., a language semantics that leaves open the order of certain evaluations. First, we reduce this problem to…
The field of Language Reasoning Models (LRMs) has been very active over the past few years with advances in training and inference techniques enabling LRMs to reason longer, and more accurately. However, a growing body of studies show that…
We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
Rankings derived from pairwise comparisons are central to many economic and computational systems. In the context of large language models (LLMs), rankings are typically constructed from human preference data and presented as leaderboards…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
This study investigates the attribution patterns underlying Chain-of-Thought (CoT) reasoning in multilingual LLMs. While prior works demonstrate the role of CoT prompting in improving task performance, there are concerns regarding the…
In this paper, we offer a guide for researchers on evaluating reasoning in language models, building the case that reasoning should be assessed through evidence of adaptive, multi-step search rather than final-answer accuracy alone. Under…
Binary multirelations can model alternating nondeterminism, for instance, in games or nondeterministically evolving systems interacting with an environment. Such systems can show partial or total functional behaviour at both levels of…
Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic trace-distribution…
A block in a linear order is an equivalence class when factored by the block relation B(x,y), satisfied by elements that are finitely far apart. We show that every computable linear order with dense condensation-type (i.e. a dense…
In this paper, we facilitate the reasoning about impure programming languages, by annotating terms with `decorations' that describe what computational (side) effect evaluation of a term may involve. In a point-free categorical…
Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this…
The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…
Document ranking experiments should be repeatable. However, the interaction between multi-threaded indexing and score ties during retrieval may yield non-deterministic rankings, making repeatability not as trivial as one might imagine. In…
Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for…