A map of dependencies among three-valued logics

International audienceThree-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value

Integration of Logic and Probability in Terminological and Inductive Reasoning

This thesis deals with Statistical Relational Learning (SRL), a research area combining principles and ideas from three important subfields of Artificial Intelligence: machine learn- ing, knowledge representation and reasoning on uncertainty. Machine learning is the study of systems that improve their behavior over time with experience; the learning process typi- cally involves a search through various generalizations of the examples, in order to discover regularities or classification rules. A wide variety of machine learning techniques have been developed in the past fifty years, most of which used propositional logic as a (limited) represen- tation language. Recently, more expressive knowledge representations have been considered, to cope with a variable number of entities as well as the relationships that hold amongst them. These representations are mostly based on logic that, however, has limitations when reason- ing on uncertain domains. These limitations have been lifted allowing a multitude of different formalisms combining probabilistic reasoning with logics, databases or logic programming, where probability theory provides a formal basis for reasoning on uncertainty. In this thesis we consider in particular the proposals for integrating probability in Logic Programming, since the resulting probabilistic logic programming languages present very in- teresting computational properties. In Probabilistic Logic Programming, the so-called "dis- tribution semantics" has gained a wide popularity. This semantics was introduced for the PRISM language (1995) but is shared by many other languages: Independent Choice Logic, Stochastic Logic Programs, CP-logic, ProbLog and Logic Programs with Annotated Disjunc- tions (LPADs). A program in one of these languages defines a probability distribution over normal logic programs called worlds. This distribution is then extended to queries and the probability of a query is obtained by marginalizing the joint distribution of the query and the programs. The languages following the distribution semantics differ in the way they define the distribution over logic programs. The first part of this dissertation presents techniques for learning probabilistic logic pro- grams under the distribution semantics. Two problems are considered: parameter learning and structure learning, that is, the problems of inferring values for the parameters or both the structure and the parameters of the program from data. This work contributes an algorithm for parameter learning, EMBLEM, and two algorithms for structure learning (SLIPCASE and SLIPCOVER) of probabilistic logic programs (in particular LPADs). EMBLEM is based on the Expectation Maximization approach and computes the expectations directly on the Binary De- cision Diagrams that are built for inference. SLIPCASE performs a beam search in the space of LPADs while SLIPCOVER performs a beam search in the space of probabilistic clauses and a greedy search in the space of LPADs, improving SLIPCASE performance. All learning approaches have been evaluated in several relational real-world domains. The second part of the thesis concerns the field of Probabilistic Description Logics, where we consider a logical framework suitable for the Semantic Web. Description Logics (DL) are a family of formalisms for representing knowledge. Research in the field of knowledge repre- sentation and reasoning is usually focused on methods for providing high-level descriptions of the world that can be effectively used to build intelligent applications. Description Logics have been especially effective as the representation language for for- mal ontologies. Ontologies model a domain with the definition of concepts and their properties and relations. Ontologies are the structural frameworks for organizing information and are used in artificial intelligence, the Semantic Web, systems engineering, software engineering, biomedical informatics, etc. They should also allow to ask questions about the concepts and in- stances described, through inference procedures. Recently, the issue of representing uncertain information in these domains has led to probabilistic extensions of DLs. The contribution of this dissertation is twofold: (1) a new semantics for the Description Logic SHOIN(D) , based on the distribution semantics for probabilistic logic programs, which embeds probability; (2) a probabilistic reasoner for computing the probability of queries from uncertain knowledge bases following this semantics. The explanations of queries are encoded in Binary Decision Diagrams, with the same technique employed in the learning systems de- veloped for LPADs. This approach has been evaluated on a real-world probabilistic ontology

Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

Logika, forma a argument

The goal of this thesis is to defend and explain the claim that traditional logical analysis is not the best tool for studying natural language argumentation. The most common critique directed at employment of logical formalisms as tools for analysis of the natural language is usually based on pointing out of differences between structure and semantics of natural languages and languages of logical formalisms. This is not the main issue, I believe. According to my findings the most fundamental problem of the traditional analysis is that it is based on many problematic epistemological assumptions, which are inherited from empiricist-positivist tradition. Namely the positivist version of the classical model of rationality as deductive reasoning from some basis of immediately verifiable and therefore unquestionable knowledge. The doctrine that every reasonable argumentation is reducible on deductions of such kinds is supposed to justify the traditional analysis of argumentation. My original contribution is mainly in showing that without abandoning those presuppositions, we cannot hope to arrive at better understanding of natural language argumentation by developing new and more precise logical formalisms. Logical formalisms are mere tools, which we have to use for the right purpose in the first place....Cílem mé disertace je obhájit a vysvětlit tezi, že tradiční logická analýza není vhodným nástrojem ke zkoumání argumentace v přirozeném jazyce. Nejčastější kritika formální logiky jako nástroje pro analýzu přirozeného jazyka je obvykle založena na poukázování na podstatné rozdíly mezi strukturou a sémantikou jazyků přirozených a jazyků logických formalismů. V tom však nevidím hlavní zdroj problémů. Podle mého úsudku je daleko zásadnějším problémem, že tradiční logická analýza často vychází z problematických epistemologických předpokladů, které analytická filosife zdědila z empiristicko- positivistické tradice. Jedná se především o pozitivistickou verzi klasického modelu racionality, jako deduktivního usuzování z nějaké báze bezprostředně ověřitelných a nepochybných poznatků. Přesvědčení, že každou rozumnou argumentaci lze redukovat na dedukci takového druhu je tím, co má ospravedlnit tradiční logickou analýzu. Můj přínos spočívá především v prokázání toho, že nezměníme-li zásadně tato východiska, pak nám pranic nepomůže, budeme-li zkoušet argumentaci v přirozeném jazyce analyzovat pomocí nových a přesnějších logických formaismů. Problém tedy není ani tak v samotném nástroji, jako spíše ve způsobu jeho užití. Pokud dostatečně zreflektujeme roli demonstrativního usuzování pro argumentaci jako...Department of LogicKatedra logikyFilozofická fakultaFaculty of Art

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