Related papers: Quantitative Strongest Post
Recent proposal for counterfactual computation [Hosten et al., Nature, 439, 949 (2006)] is analyzed. It is argued that the method does not provide counterfactual computation for all possible outcomes. The explanation involves a novel…
Code language models are increasingly adopted for both understanding and generative tasks. Despite their success, these models frequently produce overconfident incorrect predictions and underconfident correct predictions, undermining their…
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide…
Recently, a new wave of thinking-capable Large Language Models has emerged, demonstrating exceptional capabilities across a wide range of reasoning benchmarks. Early studies have begun to explore how the amount of compute in terms of the…
Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop…
Hoare's logic is an axiomatic system of proving programs correct, which has been extended to be a separation logic to reason about mutable heap structure. We develop the most fundamental logical structure of strongest postcondition of…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…