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Hyperintensional Modal Logic: Motivation, Semantic Frameworks, and Basic Theory.
Dragonová, Ivana ; Sedlár, Igor (advisor) ; Punčochář, Vít (referee)
A modal operator is hyperintensional if it does not respect the Equivalence Rule (RE), according to which if two formulas are logically equivalent, then so are the results of applying the modal operator to them. Typically, this happens when dealing with topics finer-grained than propositions, such as the notions of knowledge and belief. This thesis discusses the class of modal logics not closed under (RE) called hyperintensional modal logics and gives an overview of the semantic approaches one can use to give a suitable interpretation for this class of logics. We discuss a state-based approach first introduced by Rantala(1982) and later developed by Wansing(1990) and a structuralist approach proposed by Cresswell(1975). In the final part, we discuss a recent approach by Sedlár (2021), Pascucci and Sedlár (2023), and show that the above-mentioned state-based and structuralist approaches can both be modeled within Sedlár's hyperintensional models. We prove completeness results for the discussed hyperintensional semantic frameworks - all of them are sound and complete with respect to the smallest (hyperintensional) modal logic. 1
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Generic Approach to Updating Uncertainty: Focus on Conditioning
Kuncová, Alexandra ; Peliš, Michal (advisor) ; Sedlár, Igor (referee)
First, we consider different kinds of representation of uncertainty and the meth- ods for updating each of them by conditioning. We focus on the generic frame- work of (conditional) plausibility spaces, since it generalises all the introduced representations. Further, we select three frameworks and list the properties that need to be added to a conditional plausibility space in order to recover each of these frameworks. The main goal of this work, however, is to show how public announcement on single-agent plausibility models, ranking structures, and pos- sibility structures realised by their corresponding update mechanisms, can be embedded into the framework of conditional plausibility spaces. At the very end we briefly illustrate a general update model using plausibility measures. Keywords: belief revision, dynamic logic, epistemic logic, plausibility space, pub- lic announcement, uncertainty, update.
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Dynamic epistemic logics
Pivoňková, Martina ; Bílková, Marta (advisor) ; Sedlár, Igor (referee)
In this thesis we will deal with the logic of public announcement which is a dynamic extension of epistemic logic. First we will explain the logic of truthful public announcement for the multiagent S5 system. Then we will examine what the public announcement can look like in systems weaker than S5. We will focus namely on systems in which the T axiom is invalid and the epistemic modality is interpreted not as a "knowledge" but as a "belief". We will create new semantics of public announcement which is not necessarily truthful but it is believed to be true. We will also try to axiomatize systems that have arisen in this way. Keywords: public announcement logic, logic for belief
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Fragments of intuitionistic logic, intermediate logics and substructural logics (selected problems).
Truhlář, Pavel ; Bílková, Marta (advisor) ; Sedlár, Igor (referee)
The abstract of the diploma thesis "Positive Formulas for Some Substructural Logics" by Pavel Truhlar We will examine which distributive substructural logics, as defined in the book of Restall "An Introduction to Substructural Logics" have the same positive fragment with and without the weak excluded middle axiom. The main result of this diploma thesis is that some substructural logics have this property. We repeat the basic notions as described in the Restall's book, especially the consecution, natural deduction, frame semantics, Hilbert system. We will use the soundness and completeness theorems. We also will use the equivalence of natural deduction systems and Hilbert systems. All these important theorems are in the above mentioned Restall's book. We make the proof of our main result in the next part. We will use the semantics of frames, similarly as de Jongh and Zhao in the article "Positive Formulas in Intuitionistic and Minimal Logic". We will define the top model. After, we define the construction which converts a model to the top model. We define for each formula the positive part of it; this is the formula, which behaves the same way on the top models as the original formula. We use Hilbert type calculus to formulate our main theorem. We prove our main result using the deduction theorem for certain...
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Substructural logics for pooling information
Sedlár, Igor ; Punčochář, Vít
This paper puts forward a generalization of the account of pooling information – offered by standard epistemic logic – based on intersection of sets of possible worlds. Our account is based on information models for substructural logics and pooling is represented by fusion of information states. This approach yields a representation of\npooling related to structured communication within groups of agents. It is shown that the generalized account avoids some problematic features of the intersection-based approach. Our main technical result is a sound and complete axiomatization of a substructural epistemic logic with an operator expressing pooling.\n
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Generic Approach to Updating Uncertainty: Focus on Conditioning
Kuncová, Alexandra ; Peliš, Michal (advisor) ; Sedlár, Igor (referee)
First, we consider different kinds of representation of uncertainty and the meth- ods for updating each of them by conditioning. We focus on the generic frame- work of (conditional) plausibility spaces, since it generalises all the introduced representations. Further, we select three frameworks and list the properties that need to be added to a conditional plausibility space in order to recover each of these frameworks. The main goal of this work, however, is to show how public announcement on single-agent plausibility models, ranking structures, and pos- sibility structures realised by their corresponding update mechanisms, can be embedded into the framework of conditional plausibility spaces. At the very end we briefly illustrate a general update model using plausibility measures. Keywords: belief revision, dynamic logic, epistemic logic, plausibility space, pub- lic announcement, uncertainty, update.
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Hypothetical Judgements, Truth and Assertibility
Punčochář, Vít ; Kolman, Vojtěch (advisor) ; Sedlár, Igor (referee) ; Bílková, Marta (referee)
Vít Punčochář Dissertation: Hypothetical Judgements, Truth and Assertibility Abstract: The main topic of this thesis is the logic of indicative conditionals, i.e. sentences of the form If A then B. In classical logic, these sentences are analysed with the help of the so- called material implication. However, the analysis is problematic in many respects. Some chapters of the thesis are devoted to the explanation of the problems, which one necessarily faces when analysing conditionals with the apparatus of standard classical logic. The stress is laid upon the fact that here we are led to a paradoxical situation: some general principles of classical logic (e.g. the principle according to which one can infer If not-A then B from A or B) seem to be unquestionable, but they have very controversial consequences. In the thesis, attempts are presented to defend classical logic as well as to revise it. The approaches to the logical analysis of conditionals are classified into two basic kinds: the first one might be called ontic and the second one epistemic. The ontic approach defines all crucial semantic notions in terms of the concept of truth that is modelled in logic as a relation between sentences of a given language and states of affairs. In contrast, the epistemic approach is not based on the concept of truth...
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Dynamic epistemic logics
Pivoňková, Martina ; Bílková, Marta (advisor) ; Sedlár, Igor (referee)
In this thesis we will deal with the logic of public announcement which is a dynamic extension of epistemic logic. First we will explain the logic of truthful public announcement for the multiagent S5 system. Then we will examine what the public announcement can look like in systems weaker than S5. We will focus namely on systems in which the T axiom is invalid and the epistemic modality is interpreted not as a "knowledge" but as a "belief". We will create new semantics of public announcement which is not necessarily truthful but it is believed to be true. We will also try to axiomatize systems that have arisen in this way. Keywords: public announcement logic, logic for belief
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Logic of questions
Peliš, Michal ; Peregrin, Jaroslav (advisor) ; Sedlár, Igor (referee) ; Wiśniewski, Andrzej (referee)
Logic of Questions Michal Peliš PhD Thesis Abstract The thesis deals with logic of questions (erotetic logic), which is one of the branches of non- classical logic. In the introductory part we speak generally about formalization of questions and the newest approaches to questions in logic are summed up. We introduce a formalization based on sets of direct answers and point out the role of inferences with questions. The rest of the thesis consists of two parts that can be read independently. The first part focuses on relationships among consequence relations in inferential erotetic logic (IEL). We keep the framework of original IEL, introduced by Andrzej Wiśniewski, together with the representation of questions by sets of direct answers. Answers are strictly formulas of the declarative language. The mix of interrogatives and declaratives occours just on the level of consequences. Consequence relations with questions are defined by means of multiple-conclusion entailment among sets of declarative formulas. This way, one can work with classes of models and to make transparent some properties and relationships. We provide a general study of erotetic inferences based on IEL that is open for non-classical applications. The second part contains epistemic erotetic logic. A question is understood as a set of direct...
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