Related papers: Towards Reasoning About Properties of Imperative P…
Logical specifications are widely used to represent software systems and their desired properties. Under system degradation or environmental changes, commonly seen in complex real-world robotic systems, these properties may no longer hold…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
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…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Metaphors are everywhere. They appear extensively across all domains of natural language, from the most sophisticated poetry to seemingly dry academic prose. A significant body of research in the cognitive science of language argues for the…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…
The programming language Prolog makes declarative programming possible, at least to a substantial extent. Programs may be written and reasoned about in terms of their declarative semantics. All the advantages of declarative programming are…
Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can…
Solving puzzles in natural language poses a long-standing challenge in AI. While large language models (LLMs) have recently shown impressive capabilities in a variety of tasks, they continue to struggle with complex puzzles that demand…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
Large Language Models (LLMs) have exhibited remarkable potential across a wide array of reasoning tasks, including logical reasoning. Although massive efforts have been made to empower the logical reasoning ability of LLMs via external…
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…
We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of…
Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Large Language Models (LLMs) trained on petabytes of data are highly compressed repositories of a significant proportion of the knowledge accumulated and distilled so far. In this paper we study techniques to elicit this knowledge in the…
We describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize inductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large…