相关论文: A Reduction of Input/Output Logics to SAT
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
We describe two systems for supporting beginner students in acquiring basic skills in expressing statements in the formalism of first-order predicate logic; the first, called "math dictations", presents users with the task of formalizing a…
This paper presents rules of inference for a binary quantifier $I$ for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. $I$ binds one variable and forms a formula from two formulas.…
Controlled natural languages (CNLs) are effective languages for knowledge representation and reasoning. They are designed based on certain natural languages with restricted lexicon and grammar. CNLs are unambiguous and simple as opposed to…
A specification theory combines notions of specifications and implementations with a satisfaction relation, a refinement relation and a set of operators supporting stepwise design. We develop a complete specification framework for real-time…
In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…
SAT provers are powerful tools for solving real-sized logic problems, but using them requires solid programming knowledge and may be seen w.r.t.\ logic like assembly language w.r.t.\ programming. Something like a high level language was…
We present a comprehensive approach to the automated formalization of legal texts using large language models (LLMs), targeting their transformation into Defeasible Deontic Logic (DDL). Our method employs a structured pipeline that segments…
This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However,…
Formal ontologies are axiomatizations in a logic-based formalism. The development of formal ontologies, and their important role in the Semantic Web area, is generating considerable research on the use of automated reasoning techniques and…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
In this paper, we study logics of dependence on the propositional level. We prove that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well…
We propose an input/output conformance testing theory utilizing Modal Interface Automata with Input Refusals (IR-MIA) as novel behavioral formalism for both the specification and the implementation under test. A modal refinement relation on…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…