This paper presents a logical Style painting classifier based on evaluated Horn clauses, qualitative colour descriptors and Explanations. Three versions of $\ell $-SHE are defined, using rational Pavelka logic, and expansions of Gödel logic and product logic with rational constants: RPL, $G$ and $\sqcap $, respectively. We introduce a fuzzy representation of the more representative colour traits for the Baroque, the Impressionism and the Post-Impressionism art styles. The $\ell $-SHE algorithm has been implemented in Swi-Prolog and tested on (...) 90 paintings of the QArt-Dataset and on 247 paintings of the Paintings-91-PIB dataset. The percentages of accuracy obtained in the QArt-Dataset for each $\ell $-SHE version are 73.3%, 65.6% $) and 68.9% $). Regarding the Paintings-91-PIB dataset, the percentages of accuracy obtained for each $\ell $-SHE version are 60.2%, 48.2% $) and 57.0% $). Our logic definition for the Baroque style has obtained the highest accuracy in both datasets, for all the $\ell $-SHE versions. An important feature of the classifier is that it provides reasons regarding why a painting belongs to a certain style. The classifier also provides reasons about why outliers of one art style may belong to another art style, giving a second classification option depending on its membership degrees to these styles. (shrink)

This article examines cases that illustrate the relation of information structure to truth-conditional semantics, grammatical form, and assertoric force. Before discussing the interaction between information structure and at-issue meaning, it considers the nature of information and what constitutes information. It then looks at two aspects of the common ground, common ground content and CG management, as well as the criteria of category membership. The article also explores the varying degrees of at-issueness, the role of rhetorical opposition and but clauses, (...) as well as the variable strength of at-issue content. The landscape of non-at-issue meaning is presented, and the distinction between conventional implicature and assertorically inert entailments is highlighted using a range of distributional diagnostics. The article concludes by analysing the relation between structural focus and exhaustivity using the semantic and pragmatic approaches. (shrink)

Sentence comprehension involves maintaining and continuously integrating linguistic information and, thus, makes demands on working memory. Past research has demonstrated that semantic WM, but not phonological WM, is critical for integrating word meanings across some distance and resolving semantic interference in sentence comprehension. Here, we examined the relation between phonological and semantic WM and the comprehension of center-embedded relative clause sentences, often argued to make heavy demands on WM. Additionally, we examined the relation between phonological and semantic WM and the (...) comprehension of transitive and dative active and passive sentences, which may also draw on WM resources depending on the number of propositions that must be maintained and the difficulty of processing passive clauses. In a large sample of individuals with aphasia, we assessed whether comprehension performance on more complex vs. simpler active-passive or embedded relative clause sentences would be predicted by semantic but not phonological WM when controlling for single word comprehension. For performance on the active-passive comprehension task, we found that semantic WM, but not phonological WM, predicted comprehension of dative sentences when controlling for comprehension of transitive sentences. We also found that phonological WM, but not semantic WM, predicted mean comprehension for reversible active-passive sentences when controlling for trials with lexical distractors. On the relative clause comprehension task, consistent with prior results, we found that semantic WM, but not phonological WM, predicted comprehension of object relative clause sentences and relative clause sentences with a passive construction. However, both phonological WM and semantic WM predicted mean comprehension across all relative clause types for reversible trials when controlling for trials with lexical distractors. While we found evidence of semantic WM’s role in comprehension, we also observed unpredicted relations between phonological WM and comprehension in some conditions. Post-hoc analyses provided preliminary evidence that phonological WM maintains a backup phonological representation of the sentence that may be accessed when sentence comprehension processing is less efficient. Future work should investigate possible roles that phonological WM may play across sentence types. (shrink)

Partly motivated by description logics, poor man's logics have been proposed as an interesting fragment of modal logics. A poor man's logic is a propositional modal logic where only literals and the connectives ∧, □, and ◊ are allowed. It is known that the complexity of the satisfiability problem may drop dramatically when going from a full modal logic to the corresponding poor man's logic, e.g., in the case of modal logic K one goes from PSPACE-complete to coNP-complete. We prove (...) that it is sometimes possible to extend poor man's logics with restricted disjunctions (i.e., clauses) without increasing the computational complexity. For Horn and Krom clauses, we provide necessary and sufficient conditions for when the resulting logic is polynomial-time. Such extensions correspond to allowing a restricted use of the union operator in description logics. (shrink)

Logical forgetting is NP-complete as a decision problem even in the simple case of propositional Horn formulae, and may exponentially increase their size. A way to forget is to replace each variable to forget with the body of each clause whose head is the variable. It takes polynomial time in the single-head case: each variable is the head of at most a clause. Some formulae are not single-head but can be made so to simplify forgetting. They are called single-head (...) equivalent. The first contribution of this article is the study of a semantical characterization of single-head equivalence. Two necessary conditions are given. They are sufficient when the formula is interequivalent, that is, the formula makes two sets of variables equivalent only if they are also equivalent to their intersection. All acyclic formulae are interequivalent. The second contribution of this article is an incomplete algorithm for turning a formula single-head. In case of success, forgetting becomes possible in polynomial time and produces a polynomial-size formula, none of which is otherwise guaranteed. The algorithm is complete on interequivalent formulae. (shrink)

A generalization of conventional Horn clause logic programming is proposed in which the space of truth values is a pseudo-Boolean or Heyting algebra, whose members may be thought of as evidences for propositions. A minimal model and an operational semantics is presented, and their equivalence is proved, thus generalizing the classic work of Van Emden and Kowalski.

We develop an abstract proof calculus for logics whose sentences are ‘Horn sentences’ of the form: $(\forall X)H \Rightarrow c$ and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the ‘Horn fragment’ of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants.

We present a mathematical approach to defeasible reasoning based on arguments. This approach integrates the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. The main contribution of this paper is a precise, well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. It aims for usability rather than novelty. We prove that an order relation can be introduced among equivalence classes of arguments under the equi-specificity relation. We also prove (...) a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search space for checking specificity. In order to implement the theoretical ideas, the language is restricted to Horn clauses for the evidential context. The language used to represent defeasible rules has been restricted in a similar way. The authors intend this work to unify the various existing approaches to argument-based defeasible reasoning. (shrink)

Miller, D., G. Nadathur, F. Pfenning and A. Scedrov, Uniform proofs as a foundation for logic programming, Annals of Pure and Applied Logic 51 125–157. A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The (...) operational semantics is formalized by the identification of a class of cut-free sequent proofs called uniform proofs. A uniform proof is one that can be found by a goal-directed search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that first-order and higher-order Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that first-order and higher-order versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to first-order Horn clauses is briefly discussed. (shrink)

This volume brings together a collection of papers covering a wide range of topics in computer and cognitive science. Topics included are: the foundational relevance of logic to computer science, with particular reference to tense logic, constructive logic, and Horn clause logic; logic as the theoretical underpinnings of the engineering discipline of expert systems; a discussion of the evolution of computational linguistics into functionally distinct task levels; and current issues in the implementation of speech act theory.

Neg-Raising concerns the phenomenon by which certain negated predicates can give rise to a reading where the negation seems to take scope from an embedded clause. The standard analysis in pragma-semantic terms goes back to Bartsch and has been elaborated in Horn, Gajewski, Romoli, and many others. Recently, this standard approach has been challenged by Collins and Postal, who argue, by providing various novel arguments, that Neg-Raising involves syntactic movement of the negation from the embedded clause into the matrix (...) clause. The syntactic structure of ‘I don’t think you’re right’ would then be like: I do[n’t]i think you’re ti right, and the Neg-Raising reading would result from the interpretation of the lower copy of the negation. In this paper I present three novel arguments against this account. First, following up work by Horn, I show that Collins and Postal, and their reply to Horn, predict that every negated predicate that can license so-called Horn-clauses should receive a Neg-Raising reading, contrary to fact. Second, Collins and Postal adopt various instances of phonological deletion of negative operators—a necessary ingredient for their account—but these instances of phonological deletion cannot be independently motivated. Third, it turns out that for certain constructions, Collins and Postal must also allude to the original Bartschian approach. I further demonstrate that the standard, pragma-semantic approach to Neg-Raising actually explains the grammaticality of Horn-clauses and other phenomena, such as the distribution of negative parentheticals, that were presented by Collins and Postal as arguments in favour of the syntactic approach to Neg-Raising, equally well, if not better, than this syntactic alternative. (shrink)

A practical system of reasoning must be both correct and efficient. An efficient system which contains a large body of information can not search for the proof of a conclusion from all information available. Efficiency requires that deduction of the conclusion be carried out in a modular way using only a relatively small and quickly identified subset of the total information. One might assume that data modularity is incompatible with correctness, where a system is correct for a logic L iff (...) it proves exactly what is valid in L. We point out that modularity and correctness are indeed incompatible if the logic in question is classical. On the other hand, the two desiderata are compatible for relevance logic. Furthermore, Horn clause resolution theorem proving is modular (this helps explain its relative efficiency) and the logic for which it is correct is relevance logic not classical logic. (shrink)

This volume contains finalized versions of papers presented at an international workshop on extensions of logic programming, held at the Seminar for Natural Language Systems at the University of Tübingen in December 1989. Several recent extensions of definite Horn clause programming, especially those with a proof-theoretic background, have much in common. One common thread is a new emphasis on hypothetical reasoning, which is typically inspired by Gentzen-style sequent or natural deduction systems. This is not only of theoretical significance, but (...) also bears upon computational issues. It was one purpose of the workshop to bring some of these recent developments together. The volume covers topics such as the languages Lambda-Prolog, N-Prolog, and GCLA, the relationship between logic programming and functional programming, and the relationship between extensions of logic programming and automated theorem proving. It contains the results of the first conference concentrating on proof-theoretic approaches to logic programming. (shrink)

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments (...) made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration. (shrink)

We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratifiable logic programs, producing a semantics we (...) call weak stratified. Finally, we show weak stratified semantics coincides exactly with the three-valued approach on stratifiable programs, though the three-valued version is generally applicable, and does not require stratification assumptions. (shrink)

The general conditions of epistemic defeat are naturally represented through the interplay of two distinct kinds of entailment, deductive and defeasible. Many of the current approaches to modeling defeasible reasoning seek to define defeasible entailment via model-theoretic notions like truth and satisfiability, which, I argue, fails to capture this fundamental distinction between truthpreserving and justification-preserving entailments. I present an alternative account of defeasible entailment and show how logic programming offers a paradigm in which the distinction can be captured, allowing for (...) the modeling of a larger range of types of defeat. This is possible through a natural extension of the declarative and procedural semantics of Horn clauses. (shrink)

We explore the problems that confront any attempt to explain or explicate exactly what a primitive logical rule of inferenceis, orconsists in. We arrive at a proposed solution that places a surprisingly heavy load on the prospect of being able to understand and deal with specifications of rules that are essentiallyself-referring. That is, any rule$\rho $is to be understood via a specification that involves, embedded within it, reference to rule$\rho $itself. Just how we arrive at this position is explained by (...) reference to familiar rules as well as less familiar ones with unusual features. An inquiry of this kind is surprisingly absent from the foundations of inferentialism—the view that meanings of expressions (especially logical ones) are to be characterized by the rules of inference that govern them. (shrink)

The length of resolution proofs is investigated, relative to the model-theoretic measure of Herband complexity. A concept of resolution deduction is introduced which is somewhat more general than the classical concepts. It is shown that proof complexity is exponential in terms of Herband complexity and that this bound is tight. The concept of R-deduction is extended to FR-deduction, where, besides resolution, a function introduction rule is allowed. As an example, consider the clause P Q: conclude P) Q, where a, f (...) are new function symbols extending Herbrand's universe. P ()Q from Q) and Skolemization). By modification of a construction of Statman it is shown that FR-deductions may be nonelementarily shorter than R-deductions . Finally it is proved that FR-deduction has weaker effects only if clausal logic is restricted to Horn logic. (shrink)

On 26 February 2020, the German Constitutional Court rejected a law from 2015 that prohibited any form of ‘business-like’ assisted suicide as unconstitutional. The landmark ruling of the highest federal court emphasised the high priority given to the rights of autonomy and free personal development, both of which constitute the principle of human dignity, the first principle of the German constitution. The ruling echoes particularities of post-war Germany’s end-of-life debate focusing on patient self-determination while rejecting any discussion of active assistance (...) to die through a lethal injection administered by a doctor. This brief report discusses the ruling in the light of the broader sociopolitical and historical context of the German end-of-life debate. (shrink)

In the modern age, the political secret has acquired a bad reputation. With modern democracy’s ideal of transparency, political secrecy is identified with political crime or corruption. The article argues that this repression of secrecy in modern democracies falls short of a substantial understanding of the structure and workings of political secrecy. By outlining a genealogy of political secrecy, it elucidates the logic as well as the blind spots of a current culture of secrecy. It focuses on two fundamental logics (...) of secrecy, deduced from the Latin terms ‘ arcanum’ and ‘ secretum’. Whereas the logic of arcanum regards secrecy as a legitimate dimension of government, a modern logic of secretum is marked by an inextricable dialectics between the withdrawal and communication of knowledge, between secrecy and publicity. Here, the secret is not so much a piece of withheld knowledge as a ‘secrecy effect’ that binds the realm of secrecy to the public sphere by a dialectics of permanent suspicion and scandal. Instead of falling into the trap of this ‘secrecy effect’ it is worth taking a closer look at the tradition of thought on the arcana imperii, from Tacitus to early modern doctrines of raison d’état to Carl Schmitt. What this tradition deals with is the functionality of secrecy and its complicated relation to the law. The arcana tradition elaborates the crucial point of secrecy: its potential, but also its profound ambivalence. Secrecy opens up a discretionary space of action exempt from the rule of law, and, according to Carl Schmitt, ignores the law so as to allow it to become effective. Secrecy serves to protect and stabilize the state, but at the same time it opens a space of exception from the rule of law that breeds violence, corruption and oppression. Instead of seeing secrecy as the opposite of a political culture of transparency, it is more productive to regard secrecy as transparency's complement – a counterpart, however, that is marked by the profound paradox of being both a consolidation of and a threat to democracy. (shrink)

The treatise known as book Lambda of Aristotle’s Metaphysics has become one of the most debated issues of recent scholarship. Aristotle adresses here fundamental questions of his theory of substance, his idea of causes and principles, and his concept of motions. Furthermore, the importance of the text is due to the fact that it contains an outline of what was traditionally understood as Aristotle’s theology.

In this short response, I agree with Cavaliere’s recent invitation to consider ectogenesis, the process of gestation occurring outside the body, as a political perspective and provocation to building a world in which reproductive and care labour are more justly distributed. But I argue that much of the literature Cavaliere addresses in which scholars argue that artificial wombs may produce greater gender equality has the limitation of taking a fixed, binary and biological approach to sex and gender. I argue that (...) in taking steps toward the possibility of more just practices of caregiving and family making, we must look first not to artificial womb technologies but to addressing the ways that contemporary legal and social practices that enforce essentialising, binary ways of thinking about reproductive bodies inhibit this goal. (shrink)

Homer'sIliadis an epic poem full of war and battles, but scholars have noted that ‘[t]he Homeric poems are interested in death far more than they are in fighting’. Even though long passages of the poem, particularly the so-called ‘battle books’ (Il.Books 5–8, 11–17, 20–2), consist of little other than fighting, individual battles are often very short with hardly ever a longer exchange of blows. Usually, one strike is all it takes for the superior warrior to dispatch his opponent, and death (...) occurs swiftly. The prominence of death in Homeric battle scenes raises the question of how and in which terms dying in battle is being depicted in theIliad: for while fighting can be described in a straightforward fashion, death is an abstract concept and therefore difficult to grasp. Recent developments in cognitive linguistics have ascertained that, when coping with difficult and abstract concepts, such as emotions, the human mind is likely to resort to figurative language and particularly to metaphors. (shrink)

This target article presents a theory of human cultural learning. Cultural learning is identified with those instances of social learning in which intersubjectivity or perspective-taking plays a vital role, both in the original learning process and in the resulting cognitive product. Cultural learning manifests itself in three forms during human ontogeny: imitative learning, instructed learning, and collaborative learning – in that order. Evidence is provided that this progression arises from the developmental ordering of the underlying social-cognitive concepts and processes involved. (...) Imitative learning relies on a concept of intentional agent and involves simple perspective-taking. Instructed learning relies on a concept of mental agent and involves alternating/coordinated perspective-taking (intersubjectivity). Collaborative learning relies on a concept of reflective agent and involves integrated perspective-taking (reflective intersubjectivity). A comparison of normal children, autistic children and wild and enculturated chimpanzees provides further evidence for these correlations between social cognition and cultural learning. Cultural learning is a uniquely human form of social learning that allows for a fidelity of transmission of behaviors and information among conspecifics not possible in other forms of social learning, thereby providing the psychological basis for cultural evolution. (shrink)

The paper first analyses the Ciceronian sources of Augustine’s idea of justice, then argues that Augustine maintains a kind of “supernatural” view of politics , which leaves no room for a normative evaluation of the socio-political sphere. The specific feature of Augustine’s political “supernaturalism”, in fact, is the idea that original sin, depriving man of divine grace, prevents the earthly world from being an improvable copy of an ideal model.

Ausgehend von der Kritik einer fehlenden psychologisch informierten Subjekttheorie als Grundlage der Theorie Epistemischer Ungerechtigkeiten von Miranda Fricker wird der Begriff der Dissoziation als sozialphilosophisches Kriterium eingeführt. Die philosophische Technik der Dissoziation wird im Verhältnis zum psychologischen Verständnis des Begriffs diskutiert. Es wird die These vertreten, dass dissoziative Mechanismen und Phänomene innerpsychische und kollektive Prozesse miterklären können, die zur Genese und Aufrechterhaltung epistemischer Ungerechtigkeiten sowie insbesondere zur Persistenz von Ideologien beitragen.

In Norway, priority for health interventions is assigned on the basis of three official criteria: health benefit, resources, and severity. Responses to the COVID-19 pandemic have mainly happened through intersectoral public health efforts such as lockdowns, quarantines, information campaigns, social distancing and, more recently, vaccine distribution. The aim of this article is to evaluate potential priority setting criteria for public health interventions. We argue in favour of the following three criteria for public health priority setting: benefit, resources and improving the (...) well-being of the worse off. We argue that benefits and priority to the worse off may reasonably be understood in terms of individual well-being, rather than only health, for public health priority setting. We argue that lessons from the COVID-19 pandemic support our conclusions. Keywords: COVID-19, Prioritarianism, Priority Setting, Public Health, Severity. (shrink)

It is always a great pleasure to read a book which presents itself not solely as a solid academic exercise, but which also firmly places itself within direly needed discussions within the activist...

This article attempts to challenge those contemporary philosophical approaches to justice (and this is the majority of them) which ascribe to the notion of justice a dominant role within ethics and political philosophy. In the first section, this overestimation of justice is traced back to J.S. Mill (and to John Rawls). After having pointed out some of the essential features of the Millian (and Rawlsian) concept, I show how far these attributes are away from what we (in our everyday language) (...) mean by the word ‚justice’. Finally, I try to spell out what might be more plausibly seen as the focus of our shared moral intuition, and to highlight to which extent there is an overlap with our common idea of justice. (shrink)