Related papers: Doxastic Lukasiewicz Logic with Public Announcemen…
In this paper, we introduce a new defeasible version of propositional standpoint logic by integrating Kraus et al.'s defeasible conditionals, Britz and Varzinczak's notions of defeasible necessity and distinct possibility, along with…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…
We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
This article introduces the first comprehensive benchmark for the Polish language at this scale: LLMzSz{\L} (LLMs Behind the School Desk). It is based on a coherent collection of Polish national exams, including both academic and…
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz…
We present a completeness result for a logical system which combines stit logic and justification logic in order to represent proving activity of the agents. This logic is interpreted over the semantics introduced in earlier publications.…
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…
In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish…
We consider the Lambek calculus, or non-commutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega$-rule, and prove that the derivability problem in this calculus is…
We present a logic for reasoning with if-then formulas which involve constants for rational truth degrees from the unit interval. We introduce graded semantic and syntactic entailment of formulas. We prove the logic is complete in Pavelka…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
In this paper we consider the logics $L_n^i$ obtained from the (n+1)-valued Lukasiewicz logics $L_{n+1}$ by taking the order filter generated by i/n as the set of designated elements. In particular, the conditions of maximality and strong…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
This paper demonstrates the undecidability of a number of logics with quantification over public announcements: arbitrary public announcement logic (APAL), group announcement logic (GAL), and coalition announcement logic (CAL). In APAL we…
We analyse logic actions of Polish groups which arise in continuous logic. We extend the generalised model theory of H.Becker to the case of Polish G-spaces when G is an arbitrary Polish group.
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…