Igor Sedlár

Fine (J Philos Log 43:549–577, 2014) developed a truthmaker semantics for intuitionistic logic, which is also called exact semantics, since it is based on a relation of exact verification between states and formulas. A natural question arises as to what are the limits of Fine’s approach and whether an exact semantics of similar kind can be constructed for other important non-classical logics. In our paper, we will generalize Fine’s approach and develop an exact semantics for some substructural logics. In particular, we will provide a truthmaker semantics for the Non-associative Lambek calculus and some of its extensions. This generalization will reveal some interesting connections between Fine’s recent work on truthmaker semantics and his early work on relevant logic.

In this work, we illustrate applications of a semantic framework for non-congruential modal logic based on hyperintensional models. We start by discussing some philosophical ideas behind the approach; in particular, the difference between the set of possible worlds in which a formula is true (its intension) and the semantic content of a formula (its hyperintension), which is captured in a rigorous way in hyperintensional models. Next, we rigorously specify the approach and provide a fundamental completeness theorem. Moreover, we analyse examples of non-congruential systems that can be semantically characterized within this framework in an elegant and modular way. Finally, we compare the proposed framework with some alternatives available in the literature. In the light of the results obtained, we argue that hyperintensional models constitute a basic, general and unifying semantic framework for (non-congruential) modal logic.

Combining relevant and classical modal logic is an approach to overcoming the logical omniscience problem and related issues that goes back at least to Levesque’s well known work in the 1980s. The present authors have recently introduced a variant of Levesque’s framework where explicit beliefs concerning conditional propositions can be formalized. However, our framework did not offer a formalization of implicit belief in addition to explicit belief. In this paper we provide such a formalization. Our main technical result is a modular completeness theorem.

One way to model epistemic states of agents more realistically is to represent these states by sets of situations rather than possible worlds. In this paper we discuss representations of epistemic update in terms of situations. After linking epistemic update based on deleting epistemic accessibility arrows with update of situations, we discuss two specific kinds of public epistemic update; monotonic update in intuitionistic dynamic epistemic logic, and non-monotonic update in substructural dynamic epistemic logic. Our investigation is mainly conceptual, but leads to completeness results using reduction axioms, and lays the groundwork for future investigation into the concept of situated epistemic update.

The primary aim of the paper is to introduce a new notion of relevance of the antecedent of a true implication statement to its consequent, and to sketch a formalization of the new notion. The formalization is set up in the framework of the so called Logic of Strict Processes , as articulated by the author in collaboration with J. Podroužek. Their approach to the relevance is presented as a natural part of a wider specter of logics, including modal and relevance logics. The formalization is compared with consequence relations in normal modal logic and in the relevance logic R. In conclusion the author outlines the most important problems of LSP, which still remain open

The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics with distributive substructural logics. Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is also shown that the framework presents a natural solution to the problem of logical omniscience

This article opposes a view widely accepted in studies concerning the history of modal logic, according to which (i) the approach of C. I. Lewis towards constructing modern modal logic was purely syntactical (i.e. limited to the construction of axiomatic systems S1-S5 of propositional modal logic), and (ii) the notion of a possible world was incorporated into modern logic and philosophy mainly by authors such as Rudolf Carnap and Saul Kripke. The article presents Lewis' definition of a possible world, and his formulation of the truth-conditions of statements containing strict implication as their main connective in terms of possible worlds. The main question of the article is whether it is possible to consider Lewis' work in this area as an early stage of the development of possible world semantics, and if so, in what sense? The article concludes by answering affirmatively, due to soundness and completeness proofs with respect to S5 using Lewis' semantics

The article introduces extended models for the propositional dynamic logic PDL. In extended models, valuation assigns to every state a set of atomic formulas and a PDL program. The program is informally construed as an action preferred by a contextually fixed agent. PDL is then extended by introducing a conditional connective expressing partial correctness claims. The main contribution of the article is the observation that the partial correctness conditional is in fact a substructural implication. It is shown that a variant of the minimal distributive substructural logic DB is a fragment of PDLS, an extension of PDL that contains the partial correctness conditional and fusion. It is also shown that the main results can be extended to a specific class of positive substructural logics.

The question, whether there is a sharp difference between an analytic and a synthetic proposition, is one of the famous philosophical topics of the 20th century. The question, however, urges one to ask following questions: "What is an analytic proposition?", or „What is a synthetic proposition?“. The aim of the paper is to contribute to the discussions of the analyticity in that it tries to answer the first of the two. However, the author does not offer his own conception of analyticity. He rather offers a more detailed view on the definitions and characteristics of an analytic proposition in Kant and Frege

The paper relates evidence and justification logics, both philosophically and technically. On the philosophical side, it is suggested that the difference between the approaches to evidence in the two families of logics can be explained as a result of their focusing on two different notions of support provided by evidence. On the technical side, a justification logic with operators pertaining to both kinds of support is shown to be sound and complete with respect to a special class of awareness models. In addition, a realization theorem with respect to K is shown to hold for the logic.

The paper offers an argument against Kripke’s assertion, that it is valid for all names of natural species, that they have no connotations. The argumentation has is roots in the semantic conception of S. Kripke as articulated in his Naming and necessity. i.e., it is an „argument from inside“ the conception itself. The argument consists of two parts: setting the conditions under which the name of a natural species has a connotation; constructing a situation, in which these conditions are fulfilled

The paper outlines a generalisation of the awareness-based epistemic semantics by Fagin and Halpern. Awareness is construed as a relation between agents and pieces of information instead of formulas. The main motive for introducing the generalisation is that it shows substructural logics to be a natural component of information-based epistemic logic: substructural logics can be seen as describing the logical behaviour of pieces of information. Substructural epistemic logics are introduced and some of their properties are discussed. In addition, extensions of substructural epistemic logics invoking group-epistemic and dynamic modalities are sketched.

Pavel Cmorej has argued that the existence of unverifiable and unfalsifiable empirical propositions follows from certain plausible assumptions concerning the notions of possibility and verification. Cmorej proves, it the context of a bi-modal alethic-epistemic axiom system AM4, that (1) p and it is not verified that p is unverifiable; (2) p or it is falsified that p is unfalsifiable; (3) every unverifiable p is logically equivalent to p and it is not verifiable that p; (4) every unverifiable p entails that p is unverifiable. This article elaborates on Cmorej’s results in three ways. Firstly, we formulate a version of neighbourhood semantics for AM4 and prove completeness. This allows us to replace Cmorej’s axiomatic derivations with simple model-theoretic arguments. Secondly, we link Cmorej’s results to two well-known paradoxes, namely Moore’s Paradox and the Knowability Paradox. Thirdly, we generalise Cmorej’s results, show them to be independent of each other and argue that results (3) and (4) are independent of any assumptions concerning the notion of verification.

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided.