Related papers: Resolution in Linguistic Propositional Logic based…

This project contains two chapters. Chapter 2 has two sections. First, we define the well-formed formulas of the Language of Sentential Logic using Construction Sequences. Second, we prove the Truth Assignments using the Language of…

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…

We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…

Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…

Logic reasoning has been critically needed in problem-solving and decision-making. Although Language Models (LMs) have demonstrated capabilities of handling multiple reasoning tasks (e.g., commonsense reasoning), their ability to reason…

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…

In this paper we present a transformation of finite propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter's default logic in the framework of…

We involve a certain propositional logic based on ortholattices. We characterize the implicational reduct of such a logic and we show that its algebraic counterpart is the so-called orthosemilattice. Properties of congruences and congruence…

Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…

We present an approach towards the deep, pluralistic logical analysis of argumentative discourse that benefits from the application of state-of-the-art automated reasoning technology for classical higher-order logic. Thanks to its…

Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…

We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles…

We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…

We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…

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…

Determining semantic textual similarity is a core research subject in natural language processing. Since vector-based models for sentence representation often use shallow information, capturing accurate semantics is difficult. By contrast,…

Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…