Related papers: Logical Reasoning for Higher-Order Functions with …
We present a new approach to automated reasoning about higher-order programs by endowing symbolic execution with a notion of higher-order, symbolic values. Our approach is sound and relatively complete with respect to a first-order solver…
The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
Reachability logic has been applied to $\mathbb{K}$ rewrite-rule-based language definitions as a language-generic logic of programs. To be able to verify not just code but also distributed system designs, a new rewrite-theory-generic…
In this work, we develop a novel reasoning approach to enhance the performance of large language models (LLMs) in future occupation prediction. In this approach, a reason generator first derives a ``reason'' for a user using his/her past…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
Machine learning systems perform well on pattern matching tasks, but their ability to perform algorithmic or logical reasoning is not well understood. One important reasoning capability is algorithmic extrapolation, in which models trained…
In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by…
Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper…
Previous deforestation and supercompilation algorithms may introduce accidental termination when applied to call-by-value programs. This hides looping bugs from the programmer, and changes the behavior of a program depending on whether it…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
We contribute the first denotational semantics of polymorphic dependent type theory extended by an equational theory for general (higher-order) reference types and recursive types, based on a combination of guarded recursion and…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
We present a variant of the quantum relational Hoare logic from (Unruh, POPL 2019) that allows us to use "expectations" in pre- and postconditions. That is, when reasoning about pairs of programs, our logic allows us to quantitatively…
Domain-specific intelligence demands specialized knowledge and sophisticated reasoning for problem-solving, posing significant challenges for large language models (LLMs) that struggle with knowledge hallucination and inadequate reasoning…
Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent…
We present an extension of Logic Programming (under stable models semantics) that, not only allows concluding whether a true atom is a cause of another atom, but also deriving new conclusions from these causal-effect relations. This is…
Large Language Models (LLMs) can generate reasoning tokens before their final answer to boost performance on complex tasks. While these sequences seem like human thought processes, empirical evidence reveals that they are not a faithful…
Dynamically typed object-oriented languages enable programmers to write elegant, reusable and extensible programs. However, with the current methodology for program verification, the absence of static type information creates significant…