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The paper presents an extension of temporal epistemic logic with operators that quantify over strategies. The language also provides a natural way to represent what agents would know were they to be aware of the strategies being used by…
We prove strong completeness of a range of substructural logics with respect to a natural poset-based relational semantics using a coalgebraic version of completeness-via-canonicity. By formalizing the problem in the language of coalgebraic…
In recent years, the creation of block-structured dictionary has attracted a lot of interest. Learning such dictionaries involve two step process: block formation and dictionary update. Both these steps are important in producing an…
Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms.…
Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new…
In an article dating back in 1992, Kosta Do\v{s}en initiated a project of modal translations in substructural logics, aiming at generalizing the well-known G\"{o}del-McKinsey-Tarski translation of intuitionistic logic into {\bf S4}.…
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and…
Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…
We review the special theory of relativity kinematics and dynamics as well as the general theory of relativity under the aspect of logic.
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…
Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over…
We generalise the Blok-J\'onsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\'onsson admit, in place…
We investigate the completeness of intuitionistic logic with respect to Prawitz's proof-theoretic validity. As an intuitionistic natural deduction system, we apply atomic second-order intuitionistic propositional logic. By developing phase…
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…
This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are…
The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic $\vdash$. It turns out that the algebraic counterpart of the variable inclusion companion of a given logic $\vdash$…