104 research outputs found
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
Proof theoretic criteria for logical constancy
Logic concerns inference, and some inferences can be distinguished from others by their holding as a matter of logic itself, rather than say empirical factors. These inferences are known as logical consequences and have a special status due to the strong level of confidence they inspire. Given this importance, this dissertation investigates a method of separating the logical from the non-logical. The method used is based on proof theory, and builds on the work of Prawitz, Dummett and Read. Requirements for logicality are developed based on a literature review of common philosophical use of the term, with the key factors being formality, and the absolute generality / topic neutrality of interpretations of logical constants. These requirements are used to generate natural deduction criteria for logical constancy, resulting in the classification of certain predicates, truth functional propositional operators, first order quantifiers, second order quantifiers in sound and complete formal systems using Henkin semantics, and modal operators from the systems K and S5 as logical constants. Semantic tableaux proof systems are also investigated, resulting in the production of semantic tableaux-based criteria for logicality
Makrokonstruktionen
The study investigates adverbial structures in spoken French that combine three or more discursive elements in a complex way. These structures are modeled in accordance with the terms of construction grammar as “macro constructions.” Drawing upon an extensive corpus, this study analyzes them with regard to their local emergence in interaction and their sedimentation
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book
Dualities in modal logic
Categorical dualities are an important tool in the study of (modal) logics. They offer conceptual understanding and enable the transfer of results between the different semantics of a logic. As such, they play a central role in the proofs of completeness theorems, Sahlqvist theorems and Goldblatt-Thomason theorems. A common way to obtain dualities is by extending existing ones. For example, Jonsson-Tarski duality is an extension of Stone duality. A convenient formalism to carry out such extensions is given by the dual categorical notions of algebras and coalgebras. Intuitively, these allow one to isolate the new part of a duality from the existing part. In this thesis we will derive both existing and new dualities via this route, and we show how to use the dualities to investigate logics. However, not all (modal logical) paradigms fit the (co)algebraic perspective. In particular, modal intuitionistic logics do not enjoy a coalgebraic treatment, and there is a general lack of duality results for them. To remedy this, we use a generalisation of both algebras and coalgebras called dialgebras. Guided by the research field of coalgebraic logic, we introduce the framework of dialgebraic logic. We show how a large class of modal intuitionistic logics can be modelled as dialgebraic logics and we prove dualities for them. We use the dialgebraic framework to prove general completeness, Hennessy-Milner, representation and Goldblatt-Thomason theorems, and instantiate this to a wide variety of modal intuitionistic logics. Additionally, we use the dialgebraic perspective to investigate modal extensions of the meet-implication fragment of intuitionistic logic. We instantiate general dialgebraic results, and describe how modal meet-implication logics relate to modal intuitionistic logics
Worlds and Objects of Epistemic Space : A study of Jaakko Hintikka's modal semantics
This study focuses on meaning and knowledge by assessing a distinctive view
regarding their relation, namely the modal view of Jaakko Hintikka. The
development of this view has not been previously scrutinized. By paying close
attention to the texts of Hintikka, I show that, despite the extensive deployment of
mathematical tools, the articulation of the view remained intuitive and vague. The
study calls attention to several points at which Hintikka omits relevant details or
disregards foundational questions. Attempts are made to articulate Hintikka’s
certain ideas in a more specific manner, and new problems that result are
identified. The central claim argued for is that Hintikka’s exposition was
unsatisfactory in many respects and hence the view, as it stands, falls short in its
explanatory scope compared to current theories in the intersection of logic,
semantics, and epistemology. However, I argue that, despite its shortcomings, the
prospects of the modal view are not exhausted. This is verified by introducing a
new interpretation of the framework and by sketching new applications relevant in
philosophy of language and in epistemology. It is also pointed out that certain
early advances of the view closely resemble, and therefore anticipate, the central
tenets of the currently influential two-dimensional approaches in logic and
semantics.Tutkimus paneutuu merkityksen ja tiedon käsitteisiin tarkastelemalla Jaakko Hintikan työtä modaalisen semantiikan parissa. Tutkimus osoittaa, että Hintikka jätti modaalisen semantiikan kehitystyössään avoimeksi useita perustavia kysymyksiä ja yksityiskohtia. Tutkimuksessa pyritään artikuloimaan täsmällisemmin joitakin Hintikan näkemyksiä, ja tunnistetaan uusia syntyviä ongelmia. Keskeisenä väitteenä on, että Hintikan teoreettinen työ jäi monilta osin epätyydyttäväksi, ja siten hänen modaalinen näkemyksensä ei yllä selitysvoimaltaan ja sovelluspotentiaaliltaan samalle tasolle kuin nykyiset filosofiset teoriat, jotka operoivat logiikan, semantiikan ja epistemologian risteyskohdissa. Tästä huolimatta tutkimuksessa argumentoidaan, että Hintikan teoreettinen viitekehys tarjoaa myös uusia kiinnostavia näköaloja. Tämä todennetaan tarjoamalla Hintikan viitekehykselle uusi tulkinta, ja soveltamalla sitä uusiin kielifilosofisiin kysymyksiin. Tutkimus nostaa myös esiin kirjallisuudessa ohitetun tosiasian, että Hintikan työ ennakoi tärkeällä tavalla nykyisin vaikutusvaltaisia kaksi-dimensionaalisia lähestymistapoja logiikassa ja semantiikassa
Syntactic approaches to negative results in process algebras and modal logics
Concurrency as a phenomenon is observed in most of the current computer science
trends. However the inherent complexity of analyzing the behavior of such a system
is incremented due to the many different models of concurrency, the variety of applications and architectures, as well as the wide spectrum of specification languages and demanded correctness criteria. For the scope of this thesis we focus on state based models of concurrent computation, and on modal logics as specification languages. First we study syntactically the process algebras that describe several different concurrent behaviors, by analyzing their equational theories. Here, we use well-established techniques from the equational logic of processes to older and newer setups, and then transition to the use of more general and novel methods for the syntactical analysis of models of concurrent programs and specification languages. Our main contributions are several positive and negative axiomatizability results over various process algebraic languages and equivalences, along with some complexity results over the satisfiability of multi-agent modal logic with recursion, as a specification language.Samhliða sem fyrirbæri sést í flestum núverandi tölvunarfræði stefnur. Hins vegar er eðlislægt flókið að greina hegðun slíks kerfis- tem er aukið vegna margra mismunandi gerða samhliða, fjölbreytileikans af forritum og arkitektúr, svo og breitt svið forskrifta mælikvarða og kröfðust réttmætisviðmiða. Fyrir umfang þessarar ritgerðar leggjum við áherslu á ástandsbundin líkön af samhliða útreikningum og á formlegum rökfræði sem forskrift tungumálum. Fyrst skoðum við setningafræðilega ferlialgebrurnar sem lýsa nokkrum mismunandi samhliða hegðun, með því að greina jöfnukenningar þeirra. Hér notum við rótgróin tækni mynda jöfnunarrökfræði ferla til eldri og nýrri uppsetningar, og síðan umskipti yfir í notkun almennari og nýrra aðferða fyrir setningafræðileg greining á líkönum samhliða forrita og forskriftartungumála. Helstu framlög okkar eru nokkrar jákvæðar og neikvæðar niðurstöður um axiomatizability yfir ýmis ferli algebrumál og jafngildi, ásamt nokkrum samSveigjanleiki leiðir af því að fullnægjanleiki fjölþátta formrökfræði með endurkomu, sem a forskrift tungumál.RANNIS: `Open Problems in the Equational Logic of Processes’ (OPEL) (grant No 196050-051)
Reykjavik University research fund: `Runtime and Equational Verification of Concurrent Programs' (ReVoCoP) (grant No 222021
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
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