Logical Entailment Research Articles

Applying algorithm selection to abductive diagnostic reasoning

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.

Обобщенные описания состояний для сильных логик первого уровня

Обобщенные описания состояний для сильных логик первого уровня

Gateways to Culture: Play, Games, Metaphors, and Institutions

Abstract In this essay I develop a case for games as a primitive form of culture and an early arrival at our ancestors’ cultural gates. I analyze the modest intellectual prerequisites for game behavior including the use of metaphor, a reliance on constitutive rules, and an ability to understand the logic of entailment. In arguing for its early arrival during the late Middle and Upper Paleolithic, I develop a case for its powerful adaptive qualities in terms of both natural and sexual selection. I accept ecological dominance coupled with an increasing sense of self as primary sources of selection pressure. I show how these two factors threatened homeostatic balances ranging from low arousal and atrophy to malaise, depression, and anomie. I suggest that an antidote or adaptation was found in culturally-enhanced forms of play — that is, formal, rule-governed games. The upshot of this analysis is a broadened discussion of cultural adaptation from one that often focuses on cooperation, social complexity, and language to other fundamental issues related to survival — namely, increased leisure time, enhanced arousal needs, and the health and physical skills required for a hunter-forager existence.

Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive Variant

In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi-intuitionistic connexive multilattice logic, obtained by replacing the connectives of intuitionistic implication and co-implication with their connexive variants.

First-Degree Entailment and its Relatives

We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \(\varphi \vdash \psi \), where both \(\varphi \) and \(\psi \) are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left (or both) of the turnstile. In this way, it is possible to capture proof-theoretically not only the entailment relation of the standard four-valued Belnap’s logic, but also its dual version, as well as some of their interesting extensions. The proof systems we propose are, in a sense, of a hybrid Hilbert–Gentzen nature. We examine some important properties of these systems and establish their completeness with respect to the corresponding entailment relations.

METAVALUATIONS

AbstractThis is a general account of metavaluations and their applications, which can be seen as an alternative to standard model-theoretic methodology. They work best for what are called metacomplete logics, which include the contraction-less relevant logics, with possible additions of Conjunctive Syllogism, (A→B) & (B→C) → .A→C, and the irrelevant, A→ .B→A, these including the logic MC of meaning containment which is arguably a good entailment logic. Indeed, metavaluations focus on the formula-inductive properties of theorems of entailment form A→B, splintering into two types, M1- and M2-, according to key properties of negated entailment theorems (see below). Metavaluations have an inductive presentation and thus have some of the advantages that model theory does, but they represent proof rather than truth and thus represent proof-theoretic properties, such as the priming property, if ├ A $\vee$ B then ├ A or ├ B, and the negated-entailment properties, not-├ ∼(A→B) (for M1-logics, with M1-metavaluations) and ├ ∼(A→B) iff ├ A and ├ ∼ B (for M2-logics, with M2-metavaluations). Topics to be covered are their impact on naive set theory and paradox solution, and also Peano arithmetic and Godel’s First and Second Theorems. Interesting to note here is that the familiar M1- and M2-metacomplete logics can be used to solve the set-theoretic paradoxes and, by inference, the Liar Paradox and key semantic paradoxes. For M1-logics, in particular, the final metavaluation that is used to prove the simple consistency is far simpler than its correspondent in the model-theoretic proof in that it consists of a limit point of a single transfinite sequence rather than that of a transfinite sequence of such limit points, as occurs in the model-theoretic approach. Additionally, it can be shown that Peano Arithmetic is simply consistent, using metavaluations that constitute finitary methods. Both of these results use specific metavaluational properties that have no correspondents in standard model theory and thus it would be highly unlikely that such model theory could prove these results in their final forms.

Consequence and Normative Guidance

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.

Paraconsistent Double Negations as Classical and Intuitionistic Negations

A classical paraconsistent logic (CP), which is regarded as a modified extension of first-degree entailment logic, is introduced as a Gentzen-type sequent calculus. This logic can simulate the classical negation in classical logic by paraconsistent double negation in CP. Theorems for syntactically and semantically embedding CP into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved. The cut-elimination and completeness theorems for CP are also shown using these embedding theorems. Similar results are also obtained for an intuitionistic paraconsistent logic (IP), and several versions of Glivenko and Godel-Gentzen translation theorems are proved for CP and IP.

Interpolation Methods for Dunn Logics and Their Extensions

The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these logics to more expressive languages. We do so by relying on the mathbf{Dunn}calculus, a signed tableau calculus whose rules mirror the Dunn conditions syntactically and which characterizes the Dunn logics in a uniform way. In terms of the mathbf{Dunn} calculus, we first introduce two different interpolation methods, each of which uniformly shows that the Dunn logics have the interpolation property. One of the methods is closely related to Maehara’s method but the other method, which we call the pruned tableau method, is novel to this paper. We provide various reasons to prefer the pruned tableau method to the Maehara-style method. We then turn our attention to extensions of Dunn logics with so-called appropriate implication connectives. Although these logics have been considered at various places in the literature, a study of the interpolation properties of these logics is lacking. We use the pruned tableau method to uniformly show that these extended Dunn logics have the interpolation property and explain that the same result cannot be obtained via the Maehara-style method. Finally, we show how the pruned tableau method constructs interpolants for functionally complete extensions of the Dunn logics.

Context-aware decision making under uncertainty for voice-based control of smart home

This paper presents a framework to build home automation systems reactive to voice for improved comfort and autonomy at home. The focus of this paper is on the context-aware decision process which must reason from uncertain facts inferred from real sensor data. This framework for building context aware systems uses a hierarchical knowledge model so that different inference modules can communicate and reason with same concepts and relations. The context-aware decision module is based on a Markov Logic Network, a recent approach which make it possible to benefit from formal logical representation and to model uncertainty of this knowledge. In this work, uncertainty of the decision model has been learned from data. Although some expert systems are able to deal with uncertainty, the Markov Logic Network approach brings a unified theory for dealing with logical entailment, uncertainty and missing data. Moreover, the ability to use a priori knowledge and to learn weights and structure from data make this model appealing to address the challenge of adaptation of expert systems to new applications. Finally, the framework has been implemented in an on-line system which has been evaluated in a real smart home with real naive users. Results of the experiment show the interest of context-aware decision making and the advantages of a statistical relational model for the framework.

How to Avoid a Robotic Apocalypse: A Consideration on the Future Developments of AI, Emergent Consciousness, and the Frankenstein Effect

One of the greatest compliments I've ever received came from a gentleman who approached me after I had delivered a paper in Vancouver, British Columbia. He said: "You're from the future, aren't you?" He was responding to the manner in which I had considered logical entailments of how future episodes may play out. Although I was trained as a philosopher of science, the majority of my work for the last two decades has been interdisciplinary and collaborative with other fields in the social and physical sciences. As a pioneer in my field - sometimes referred to as experimental philosophy - I often employ the use of thought experiments or "what if?" scenarios to imagine possible future worlds. Thought experiments have been around for thousands of years; from Plato's allegory of the cave (Figure 1), to Rene Descartes' malin genie (Figure 2), to Hilary Putnam's brains in vats (Figure 3).

A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.

Logic of approximate entailment in quasimetric and in metric spaces

It is known that a quasimetric space can be represented by means of a metric space; the points of the former space become closed subsets of the latter one, and the role of the quasimetric is assumed by the Hausdorff quasidistance. In this paper, we show that, in a slightly more special context, a sharpened version of this representation theorem holds. Namely, we assume a quasimetric to fulfil separability in the original sense due to Wilson. Then any quasimetric space can be represented by means of a metric space such that distinct points are assigned disjoint closed subsets.This result is tailored to the solution of an open problem from the area of approximate reasoning. Following the lines of E. Ruspini’s work, the Logic of Approximate Entailment (mathsf {LAE}) is based on a graded version of the classical entailment relation. We present a proof calculus for mathsf {LAE} and show its completeness with regard to finite theories.

Relational semantics for the 4-valued relevant logics BN4 and E4

The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of (relevant) entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.

A companion to Brady's 4-valued relevant logic BN4: The 4-valued logic of entailment E4

Brady's logic BN4 can be viewed as the 4-valued logic of the relevant conditional. The aim of this article is to introduce the logic E4, which can be regarded as the 4-valued logic of (relevant) entailment on the basis of the two following facts: (1) as the logic R-mingle, E4 has the ‘quasi-relevance property’; (2) as Anderson and Belnap's logic of entailment E, E4 encloses a sound theory of logical necessity when the necessity operator is introduced via the definition □A=df(A→A)→A .

Logics for Approximate Entailment in ordered universes of discourse

The Logic of Approximate Entailment ( LAE ) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an order structure. The chosen framework is designed in view of possible applications. • We consider a variant of the Logic of Approximate Entailment in the sense of Ruspini. • Propositions are interpreted by subsets of a chain, or a product of chains. • We present the calculi LAEC and LAEPC and show their completeness. • In these calculi, it is possible to combine conclusions in a conjunctive way.

Mapping-equivalence and oid-equivalence of single-function object-creating conjunctive queries

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. The single-function symbol can be used only once in the head of the query. 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.

The logic determined by Smiley’s matrix for Anderson and Belnap’s first-degree entailment logic

The aim of this paper is to define the logical system Sm4 characterised by the degree of truth-preserving consequence relation defined on the ordered set of values of Smiley’s four-element matrix MSm4. The matrix MSm4 has been of considerable importance in the development of relevant logics and it is at the origin of bilattice logics. It will be shown that Sm4 is a most interesting paraconsistent logic which encloses a sound theory of logical necessity similar to that of Anderson and Belnap’s logic of entailment E. Intuitively, Sm4 can be described as a four-valued expansion of the positive fragment of Lewis’ S5 or, alternatively, as a four-valued version of S5.

Logic of approximate entailment in quasimetric spaces

The logic LAE q discussed in this paper is based on an approximate entailment relation. LAE q generalises classical propositional logic to the effect that conclusions can be drawn with a quantified imprecision. To this end, properties are modelled by subsets of a distance space and statements are of the form that one property implies another property within a certain limit of tolerance. We adopt the conceptual framework defined by E. Ruspini; our work is towards a contribution to the investigation of suitable logical calculi. LAE q is based on the assumption that the distance function is a quasimetric. We provide a proof calculus for LAE q and we show its soundness and completeness for finite theories. As our main tool for showing completeness, we use a representation of proofs by means of weighted directed graphs. • We propose an axiomatisation of Approximate Reasoning in the sense of E. Ruspini's paper “On the semantics of fuzzy logic”. • The Logic LAE q deals with statements of the form that a property implies another one within a specified limit of tolerance. • We present a proof calculus for LAE q and show its soundness and completeness.

The Deductive-Nomological Account of Metaphysical Explanation

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.