Related papers: Inputs, Outputs, and Composition in the Logic of I…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
Tarski's semantic definition of truth is the composition of its extensional and intensional aspects. Abstract satisfaction, the core of the semantic definition of truth, is the basis for the theory of institutions (Goguen and Burstall). The…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
FLUX is a programming method for the design of agents that reason logically about their actions and sensor information in the presence of incomplete knowledge. The core of FLUX is a system of Constraint Handling Rules, which enables agents…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
Large reasoning models (LRMs) generate complex reasoning traces with planning, reflection, verification, and backtracking. In this work, we introduce ReasoningFlow, a unified schema for analyzing the semantic structures of these complex…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
We present a novel reasoning approach called Flow-of-Options (FoO), designed to address intrinsic biases in Large Language Models (LLMs). Flow-of-Options enables LLMs to systematically explore a diverse range of possibilities in their…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and…
We present the Flow-Limited Authorization First-Order Logic (FLAFOL), a logic for reasoning about authorization decisions in the presence of information-flow policies. We formalize the FLAFOL proof system, characterize its proof-theoretic…
Information flow guided synthesis is a compositional approach to the automated construction of distributed systems where the assumptions between the components are captured as information-flow requirements. Information-flow requirements are…
Life depends as much on the flow of information as on the flow of energy. Here we review the many efforts to make this intuition precise. Starting with the building blocks of information theory, we explore examples where it has been…
Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their…
We reconsider the persistence of information under the dynamics of the logistic map in order to discuss communication through a nonlinear channel where the sender can set the initial state of the system with finite resolution, and the…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
Understanding how information is dynamically accumulated and transformed in human reasoning has long challenged cognitive psychology, philosophy, and artificial intelligence. Existing accounts, from classical logic to probabilistic models,…
We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…