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Статья посвящена рассмотрению одного из решений скептического парадокса Витгенштейна-Крипке. В статье приводится краткое объяснение парадокса относительно значений языковых выражений и анализируется его решение путём применения метода математической индукции, предложенное В. А. Ладовым. Я показываю уязвимость такого решения, связанную с понятием логического следования и ω-аргументом А. Тарского, а также ставлю ряд вопросов, касающихся статуса математики и философского объяснения математического языка. В заключении намечается два варианта преодоления ω-аргумента в контексте скептического парадокса., The paper deals with one of the solutions of the WittgensteinKripke skeptical paradox. The paper gives a brief explanation of the paradox concerning the meanings of linguistic expressions and analyses its solution by means of mathematical induction proposed by V. A. Ladov. I show the vulnerability of such a solution connected with the notion of logical entailment and A. Tarski's ω-argument. Also, I raise some questions concerning the status of mathematics and the relation of mathematics with its language. The conclusion outlines two options for overcoming the ωargument in the context of the skeptical paradox.

This paper discusses the uniqueness thesis , a core thesis in the epistemology of disagreement. After presenting uniqueness and clarifying relevant terms, a novel counterexample to the thesis will be introduced. This counterexample involves logical disagreement . Several objections to the counterexample are then considered, and it is argued that the best responses to the counterexample all undermine the initial motivation for uniqueness.

Logic arguably plays a role in the normativity of reasoning. In particular, there are plausible norms of belief/disbelief whose antecedents are constituted by claims about what follows from what. But is logic also relevant to the normativity of agnostic attitudes? The question here is whether logical entailment also puts constraints on what kinds of things one can suspend judgment about. In this paper I address that question and I give a positive answer to it. In particular, I advance two logical norms of agnosticism, where the first one allows us to assess situations in which the subject is agnostic about the conclusion of a valid argument and the second one allows us to assess situations in which the subject is agnostic about one of the premises of a valid argument.

The complexity of technical systems requires increasingly advanced fault diagnosis methods to ensure safety and reliability during operation. Particularly in domains where maintenance constitutes an extensive portion of the entire operation cost, efficient and effective failure identification holds the potential to provide large economic value. Abduction offers an intuitive concept for diagnostic reasoning relying on the notion of logical entailment. Nevertheless, abductive reasoning is an intractable problem and computing solutions for instances of reasonable size and complexity persists to pose a challenge. In this paper, we investigate algorithm selection as a mechanism to predict the “best” performing technique for a specific abduction scenario within the framework of model-based diagnosis. Based on a set of structural attributes extracted from the system models, our meta-approach trains a machine learning classifier that forecasts the most runtime efficient abduction technique given a new diagnosis problem. To assess the predictor’s selection capabilities and the suitability of the meta-approach in general, we conducted an empirical analysis featuring seven abductive reasoning approaches. The results obtained indicate that applying algorithm selection is competitive in comparison to always choosing a single abductive reasoning method.

Logic, the tradition has it, is normative for reasoning. But is that really so? And if so, in what sense is logic normative for reasoning? As Gilbert Harman has reminded us, devising a logic and devising a theory of reasoning are two separate enterprises. Hence, logic's normative authority cannot reside in the fact that principles of logic just are norms of reasoning. Once we cease to identify the two, we are left with a gap. To bridge the gap one would need to produce what John MacFarlane has appropriately called a 'bridge principle', i.e. a general principle articulating a substantive and systematic link between logical entailment and norms of reasoning. This is Harman's skeptical challenge. In this paper, I argue that Harman's skeptical challenge can be met. I show how candidate bridge principles can be systematically generated and evaluated against a set of well-motivated desiderata. Moreover, I argue that bridge principles advanced by MacFarlane himself and others, for all their merit, fail to address the problem originally set forth by Harman and so do not meet the skeptical challenge. Finally, I develop a bridge principle that meets Harman's requirements as well as being substantive.

This paper presents a way in which formal logic can be understood and reformulated in terms of argumentation that can help us unify formal and informal reasoning. Classical deductive reasoning will be expressed entirely in terms of notions and concepts from argumentation so that formal logical entailment is equivalently captured via the arguments that win between those supporting concluding formulae and arguments supporting contradictory formulae. This allows us to go beyond Classical Logic and smoothly connect it with human reasoning, thus providing a uniform argumentation-based view of both informal and formal logic., Cet article montre comment la logique formelle peut être comprise et reformulée en termes d'argumentation de manière à nous aider à unifier le raisonnement formel et non formel. Le raisonnement déductif classique sera entièrement exprimé en termes de notions et de concepts issus de l'argumentation, de sorte que l'implication logique formelle soit saisie de manière équivalente via les arguments gagnants entre ceux qui soutiennent les formules de conclusion et ceux qui soutiennent des formules contradictoires. Cela nous permet d'aller au-delà de la logique classique et de la relier facilement au raisonnement humain, fournissant ainsi une vision uniforme, basée sur une argumentation, de la logique non formelle et formelle.

The paper explores a deductive-nomological account of metaphysical explanation: some truths metaphysically explain, or ground, another truth just in case the laws of metaphysics determine the latter truth on the basis of the former. I develop and motivate a specific conception of metaphysical laws, on which they are general rules that regulate the existence and features of derivative entities. I propose an analysis of the notion of ‘determination via the laws’, based on a restricted form of logical entailment. I argue that the DN-account of ground can be defended against the well-known objections to the DN-approach to scientific explanation. The goal of the paper is to show that the DN-account of metaphysical explanation is a well-motivated and defensible theory.

Embedding knowledge graphs (KGs) into continuous vector spaces is a focus of current research. Early works performed this task via simple models developed over KG triples. Recent attempts focused on either designing more complicated triple scoring models, or incorporating extra information beyond triples. This paper, by contrast, investigates the potential of using very simple constraints to improve KG embedding. We examine non-negativity constraints on entity representations and approximate entailment constraints on relation representations. The former help to learn compact and interpretable representations for entities. The latter further encode regularities of logical entailment between relations into their distributed representations. These constraints impose prior beliefs upon the structure of the embedding space, without negative impacts on efficiency or scalability. Evaluation on WordNet, Freebase, and DBpedia shows that our approach is simple yet surprisingly effective, significantly and consistently outperforming competitive baselines. The constraints imposed indeed improve model interpretability, leading to a substantially increased structuring of the embedding space. Code and data are available at https://github.com/iieir-km/ComplEx-NNE_AER., Comment: To appear in ACL 2018

Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning decidable or even tractable. While a number of such logics have been proposed in the past, they tend to remain for theoretical analysis only and their practical relevance is very limited. In this paper, we aim to go beyond the theory. Building on earlier work by Liu, Lakemeyer, and Levesque, we develop a logic of limited belief that is highly expressive while remaining decidable in the first-order and tractable in the propositional case and exhibits some characteristics that make it attractive for an implementation. We introduce a reasoning system that employs this logic as representation language and present experimental results that showcase the benefit of limited belief., Comment: 22 pages, 0 figures, Twenty-sixth International Joint Conference on Artificial Intelligence (IJCAI-17)

This paper synthesizes confirmation by instances and confirmation by successful predictions, and thereby the Hempelian and the hypothetico-deductive traditions in confirmation theory. The merger of these two approaches is subsequently extended to the piecemeal confirmation of entire theories. It is then argued that this synthetic account makes a useful contribution from both a historical and a systematic perspective.

This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a class of models in which systems are taken to be primitive elements but bear certain relations to one another. I prove soundness and completeness for S2 over this class of models and argue that this semantics makes sense of at least a substantial fragment of Lewis's logical theory.

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w , where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w , for all w, and give some formal properties of it. National Science Centre, Poland, numbers of grants: 2015/19/B/HS1/02478, 2015/19/N/HS1/02401.

We present a novel logic-based framework to automate multi-issue bilateral negotiation in e-commerce settings. The approach exploits logic as communication language among agents, and optimization techniques in order to find Pareto-efficient agreements. We introduce $${\mathcal{P}}({\mathcal{N}})$$ , a propositional logic extended with concrete domains, which allows one to model relations among issues (both numerical and non-numerical ones) via logical entailment, differently from well-known approaches that describe issues as uncorrelated. Through $${\mathcal{P}}({\mathcal{N}})$$ it is possible to represent buyer's request, seller's supply and their respective preferences as formulas endowed with a formal semantics, e.g., "if I spend more than 30000 � for a sedan then I want more than a two-years warranty and a GPS system included". We mix logic and utility theory in order to express preferences in a qualitative and quantitative way. We illustrate the theoretical framework, the logical language, the one-shot negotiation protocol we adopt, and show we are able to compute Pareto-efficient outcomes, using a mediator to solve an optimization problem. We prove the computational adequacy of our method by studying the complexity of the problem of finding Pareto-efficient solutions in our setting.

Conjunctive database queries have been extended with a mechanism for object creation to capture important applications such as data exchange, data integration, and ontology-based data access. Object creation generates new object identifiers in the result, that do not belong to the set of constants in the source database. The new object identifiers can be also seen as Skolem terms. Hence, object-creating conjunctive queries can also be regarded as restricted second-order tuple-generating dependencies (SO tgds), considered in the data exchange literature. In this paper, we focus on the class of single-function object-creating conjunctive queries, or sifo CQs for short. We give a new characterization for oid-equivalence of sifo CQs that is simpler than the one given by Hull and Yoshikawa and places the problem in the complexity class NP. Our characterization is based on Cohen's equivalence notions for conjunctive queries with multiplicities. We also solve the logical entailment problem for sifo CQs, showing that also this problem belongs to NP. Results by Pichler et al. have shown that logical equivalence for more general classes of SO tgds is either undecidable or decidable with as yet unknown complexity upper bounds., Comment: This revised version has been accepted on 11 January 2016 for publication in The VLDB Journal

I explore the nature of lacunae problems from the analysis of the concepts of Larry Laudan, Theo Kuipers and Atocha Aliseda, respectively, on the matter. I will suggest that lacunae problems may arise from the weakening of the notion of ‘empirical failure’ and to have repercussions on the notion of ‘logical entailment’. Se explora la naturaleza de los problemas lacunae a partir del análisis de los conceptos elaborados, respectivamente, por Larry Laudan, Theo Kuipers y Atocha Aliseda. Sugeriré que los problemas lacunae pueden surgir del debilitamiento de la noción de ‘falsación empírica’ y repercutir en la noción de ‘implicación lógica’.

The conflict between science and religion is not irremediable: the world concept of science is changing, and the change brings about a rapprochement with religious beliefs in some fundamental areas. One such area is the question of original creation. Recent findings regarding the nature of the universe show the improbability of its having arisen in the course of a random process. The perennial religious intuition of a transcendental act of creation is a logical entailment of the randomly entirely improbable fine tuning of the natural laws and processes that the observed universe manifests.

Large-scale knowledge graphs such as those in the Linked Data cloud are typically represented as subject-predicate-object triples. However, many facts about the world involve more than two entities. While n-ary relations can be converted to triples in a number of ways, unfortunately, the structurally different choices made in different knowledge sources significantly impede our ability to connect them. They also make it impossible to query the data concisely and without prior knowledge of each individual source. We present FrameBase, a wide-coverage knowledge-base schema that uses linguistic frames to seamlessly represent and query n-ary relations from other knowledge bases, at different levels of granularity connected by logical entailment. It also opens possibilities to draw on natural language processing techniques for querying and data mining.

A framework is proposed in which information about images(s form and information about image’s content are addressed in a principled way. The framework relies on the an uncertainty description logic U-ALC, which is also newly proposed in this paper, for (i) representing the semantics of images and (ii) for defining the retrieval process in terms of logical entailment. The overall framework thus extends current image retrieval systems with the use of qualitative uncertainty semantic information processing.

We present a sound and complete model of lambda-calculus reductions based on structures inspired by modal logic (closely related to Kripke structures). Accordingly we can construct a logic which is sound and complete for the same models, and we identify lambda-terms with certain simple sentences (predicates) in this logic, by direct compositional translation. Reduction then becomes identified with logical entailment. Thus, the models suggest a new way to identify logic and computation. Both have elementary and concrete representations in our models; where these representations overlap, they coincide. In a concluding speculation, we note a certain subclass of the models which seems to play a role analogous to that played by the cumulative hierarchy models in axiomatic set theory and the natural numbers in formal arithmetic -- there are many models of the respective theories, but only some, characterised by a fully second order interpretation, are the 'intended' ones.

In this paper we seek an explanation for the preference to use adversative connectives when reinforcing some implicatures. We begin by examining, and rejecting, an hypothesis according to which the nature of the implicatures can encode their argumentative properties. We then argue that this constraint is not due to the nature of the inferences at hand but rather to distinct argumentative relations between the propositions expressed in the discourse. We provide a solution in an argumentative framework and then extend our observations to cases including an overt restriction rather than implicatures. We conclude by looking at various explanations for the source of the preference we observe.

Several notions of redundancy exist for Association Rules. Often, these notions take the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant"; if we see datasets as interpretations (or models) in the logical sense, this is a form of logical entailment. In many logics, entailment has a syntactic counterpart in the form of a deduction calculus. We provide such a deduction calculus for existing notions of redundancy; then, we consider a very general notion of entailment, where a confidence threshold is fixed and several rules can act as simultaneous premises, and identify exactly the cases where a partial rule follows from two partial rules; we also give a deduction calculus for this setting.

I think that it is very proper to include a paper about truth in a volume dedicated to Jaakko Hintikka even if it does not deal directly with his highly original ideas about this topic that are related to IF logic. This essay considers the problem of truth in a conservative way, so to speak way. I will focus on properties of the predicate ‘is true’ derived from very elementary logical insights. It is convenient to start with Frege’s view (see Frege 1979a, Frege 1979b) that logic is the science of truth. This thesis should be understood to mean that logic concerns formal principles of truth (the distinction between formal truth and material truth was very common in German philosophy of the 19 century). Putting this in more contemporary terminology, formal truth consists in truth defined by purely structural criteria and transmitted by principles of logical entailment (logical consequence) as codified by logical calculus. These principles always guarantee the truth of conclusion if premises are true; technically speaking, logical entailment preserves truth, that is, transmits it from premises to conclusion. Is the view that logic is the science of truth the only possibility? Surprisingly enough, the answer is no, because it is not difficult to define the consequence relation as preserving falsehood (see also Wolenski 1995). Consider the formulas

In this paper we analyze the Strawson’s notion of presupposition proposed in his book Introduction to Logical Theory. Strawsonian notion of presupposition is dependent on the notion of logical entailment. We make use of the theory of logical consequence operation as a general framework to show that it is impossible to find a logical consequence operation which mirrors the philosophical intuitions of the Strawson’s notions of presupposition. The aim of this paper is to present in details the philosophical backgrounds of the formal analysis presented in the author’s paper “Strawsonian presuppositions and logical entailment”.

The paper features MAVE, a knowledge-based system for answer validation through deep linguistic processing and logical inference. A relaxation loop is used to determine a robust indicator of logical entailment. The system not only validates answers directly, but also gathers evidence by proving the original question and comparing results with the answer candidate. This method boosts recall by up to 13%. Additional indicators signal false positives. The filter increases precision by up to 14.5% without compromising recall of the system.

We present a novel approach to knowledge-based automated one-shot multi-issue bilateral negotiation handling, in a homogeneous setting, both numerical features and non-numerical ones. To this aim we introduce P(N), a propositional logic extended with concrete domains, which allows to: model relations among issues (both numerical and not numerical ones) via logical entailment, differently from well-known approaches that describe issues as uncorrelated; represent buyer's request, seller's supply and their respective preferences as formulas endowed with a formal semantics.