相关论文: Self-referentiality in Justification Logic
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…
We present a logic for the reasoning about necessity and justifications which is independent from relational semantics. We choose the concept of justification -- coming from a class of "Justification Logics" (Artemov 2008, Fitting 2009) --…
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an…
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 study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing…
A Henkin-style proof of completeness of first-order classical logic is given with respect to a very small set (notably missing cut rule) of Genzten deduction rules for intuitionistic sequents. Insisting on sparing on derivation rules,…
Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can…
The framework of cyclic proof systems provides a reasonable proof system for logics with inductive definitions. It also offers an effective automated proof search procedure for such logics without finding induction hypotheses. Recent…
Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into…
In recent years, the effort to formalize erotetic inferences---i.e., inferences to and from questions---has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
Reasoning with minimal models has always been at the core of many knowledge representation techniques, but we still have only a limited understanding of this problem in Description Logics (DLs). Minimization of some selected predicates,…
Large language models sometimes produce structured, first-person descriptions that explicitly reference awareness or subjective experience. To better understand this behavior, we investigate one theoretically motivated condition under which…
This paper investigates the reliability of explanations generated by large language models (LLMs) when prompted to explain their previous output. We evaluate two kinds of such self-explanations - extractive and counterfactual - using three…
Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…