Many philosophers take purportedly logical cases of ground ) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be (...) a species of ground even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground. (shrink)

I identify a notion of logical grounding, clarify it, and show how it can be used (i) to characterise various consequence relations, and (ii) to give a precise syntactic account of the notion of “groundedness” at work in the literature on the paradoxes of truth.

Existential claims are widely held to be grounded in their true instances. However, this principle is shown to be problematic by arguments due to Kit Fine. Stephan Krämer has given an especially simple form of such an argument using propositional quantifiers. This note shows that even if a schematic principle of existential grounds for propositional quantifiers has to be restricted, this does not immediately apply to a corresponding non-schematic principle in higher-order logic.

According to an intuitive picture of relevant entailment, an entailment is relevant if all the formulas it contains contribute to its validity. In this paper, we provide a ground-theoretic analysis of this notion of contribution, and as a result of relevant entailment. We build a system of bilateral logical grounding within which we can derive classical entailment and analyze the contribution of premises and conclusions, in terms of a certain type of connection between their respective logical grounds. (...) The resulting framework is shown to have a strong unifying and explanatory power by bringing together the notions of grounding and relevance and explaining the commonalities and differences between alternative contribution-based accounts of relevance. (shrink)

If Andrea knows that Biden won the last presidential election, then they also know that either Biden won the last presidential election, or Biden is a reptilian. This is the response that epistemic logics based on standard Kripke relational semantics provide, which is consistent with the fact that minimally rational agents can perform disjunction introduction. This is not the case in topic-sensitive semantics though. An agent might not grasp the concept of what a reptilian is, and therefore not be able (...) to know any proposition dealing with reptilians. By employing the concept of logical grounding, I propose a semantics that keeps the requirement of topic-grasping but weakens it, re-establishing a more standard treatment of disjunction, in line with the capacities of minimally rational agents. The paper is structured as follows. In Section 2 I introduce topic-sensitive semantics. In Section 3 I introduce the concept of logical grounding – focusing on the grounds of disjunction – and motivate some desiderata. The concept of minimal topic, the core of my proposal, is detailed in Section 4 and exploited in Section 5 to propose a new topic-sensitive semantic clause for knowledge. I conclude in Section 6. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found in human (...) reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

We formally investigate immediate and mediate grounding operators from an inferential perspective. We discuss the differences in behaviour displayed by several grounding operators and consider a general distinction between grounding and logical operators. Without fixing a particular notion of grounding or grounding relation, we present inferential rules that define, once a base grounding calculus has been fixed, three grounding operators: an operator for immediate grounding, one for mediate grounding – corresponding to the transitive closure of the immediate grounding one (...) – and a grounding tree operator, which enables us to internalise chains of immediate grounding claims without losing any information about them. We then present an in-depth proof-theoretical study of the introduced rules by focussing, in particular, on the question whether grounding operators can be considered as logical operators and whether balanced rules for grounding operators can be defined. (shrink)

In this paper, we will explore two initiatives that focus on the importance of employing logical theories in educating people how to think and reason properly, one in Poland: The Lvov-Warsaw School; the other in North America: The Informal Logic Initiative. These two movements differ in the logical means and skills that they focus on. However, we believe that they share a common purpose: to educate students in logic and reasoning (logical education conceived as a process) so (...) that they may be able to apply their skills to analyze the issues in their society (logical culture as a result of logical education). The aim of the paper is to justify this claim by exploring research objectives and products that are common to both movements. (shrink)

In this paper, I seek to undermine G.A. Cohen ’s polemical use of a metaethical claim he makes in his article, ‘ Facts and Principles’, by arguing that that use requires an unsustainable equivocation between epistemic and logical grounding. I begin by distinguishing three theses that Cohen has offered during the course of his critique of Rawls and contractualism more generally, the foundationalism about grounding thesis, the justice as non-regulative thesis, and the justice as all-encompassing thesis, and briefly argue (...) that they are analytically independent of each other. I then offer an outline of the foundationalism about grounding thesis, characterising it, as Cohen does, as a demand of logic. That thesis claims that whenever a normative principle is dependent on a fact, it is so dependent in virtue of some other principle. I then argue that although this is true as a matter of logic, it, as Cohen admits, cannot be true of actual justifications, since logic cannot tell us anything about the truth as opposed to the validity of arguments. Facts about a justification cannot then be decisive for whether or not a given argument violates the foundationalism about grounding thesis. As long as, independently of actual justifications, theorists can point to plausible logically grounding principles, as I argue contractualists can, Cohen ’s thesis lacks critical bite. (shrink)

I explore the logic of ground. I first develop a logic of weak ground. This logic strengthens the logic of weak ground presented by Fine in his ‘Guide to Ground.’ This logic, I argue, generates many plausible principles which Fine’s system leaves out. I then derive from this a logic of strict ground. I argue that there is a strong abductive case for adopting this logic. It’s elegant, parsimonious and explanatorily powerful. Yet, so I suggest, (...) adopting it has important consequences. First, it means we should think of ground as a type of identity. Second, it means we should reject much of Fine’s logic of strict ground. I also show how the logic I develop connects to other systems in the literature. It is definitionally equivalent both to Angell’s logic of analytic containment and to Correia’s system G. (shrink)

The relation between logic and rationality has recently re-emerged as an important topic of discussion. Following the ideas of Broome [1999] and MacFarlane [2004], the debate focused on providing rational requirements, which work as bridges between logic and epistemic norms. However, as Broome [2014] and Way [2011] observed, the usual requirements cannot capture some important aspects of rationality, such as how one can rationally believe something on the basis of believing something else. Broome [2014] proposed a few additional principles for (...) this purpose. In this paper I develop a more systematic family of basing permissions using the recent notion of grounding. In particular, I claim that if Γ grounds A, and you believe Γ, then rationality permits you to believe A on the basis of believing Γ. (shrink)

In his 2010 paper ‘Grounding and Truth-Functions’, Fabrice Correia has developed the first and so far only proposal for a logic of ground based on a worldly conception of facts. In this paper, we show that the logic allows the derivation of implausible grounding claims. We then generalize these results and draw some conclusions concerning the structural features of ground and its associated notion of relevance, which has so far not received the attention it deserves.

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many-many case, giving rise (...) to the Pure Logic of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete. (shrink)

This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical computer science.

The concept of grounding - of a fact obtaining in virtue of other facts - has been a topic of intensive philosophical and logical investigation over roughly the past two decades. Many philosophers take grounding to deserve a central place in metaphysical theorizing, in great part because it is thought to do a better job than other concepts - for example, reduction and supervenience - at capturing certain phenomena. Studies on the logic of grounding have largely been conducted with (...) this philosophical background in mind. In this Element, the author tries to give a faithful picture of the contemporary development of the logic of grounding in a way that is both reasonably comprehensive and reasonably systematic. (shrink)

The article reports findings of a study conducted to explore the cognitive moral logics used for considering software piracy as ethical or unethical. Since the objective was to elicit the moral logics from the respondents, semi-structured in-depth interviews of 38 software professionals of India were conducted. The content of the interviews was analyzed using the grounded theory framework which does not begin with constructs and their interlinkages and then seek proof instead it begins with an area of study and allows (...) them to emerge from that area of study. Given the objective of exploring moral logics, grounded theory seemed an appropriate choice. Results revealed that 21 respondents considered software piracy unethical whereas 17 did not. Though economic reasons formed the most fundamental logic in both the cases, an overall analysis revealed that the respondents mostly used moral justification (neutralization) for not considering software piracy unethical whereas those considering it unethical used normative (principled) logics. The interconnections among logics are analyzed and results are discussed along with the limitations of the study. (shrink)

This article develops the Pure Logic of Iterated Full Ground (PLIFG), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction (...) rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle. (shrink)

In this paper, I situate Logical Argument Mapping within.

A propositional framework of formal reasoning is proposed, which emphasises the pattern of entering and exiting context. Contexts are modelled by an algebraic structure which reflects the order and manner in which context is entered into and exited from.The equations of the algebra partitions context terms into equivalence classes. A formal semantics is defined, containing models that map equivalence classes of certain context terms to sets of interpretations of the formula language. The corresponding Hilbert system incorporates the algebraic equations as (...) axioms asserted in context.In semigroups of contexts, where combination of contexts is associative, finite ground algebraic equations correspond to contingent equivalence between certain logical formulas. Systems for sets and multisets of contexts are obtained by presenting their respective algebras as associativity plus finite ground equations. Soundness and completeness results are proved.Some contextual reasoning systems in the literature are inherently associative, and we present those as special cases. (shrink)

Many philosophers have been attracted to the idea of using the logical form of a true sentence as a guide to the metaphysical grounds of the fact stated by that sentence. This paper looks at a particular instance of that idea: the widely accepted principle that disjunctions are grounded in their true disjuncts. I will argue that an unrestricted version of this principle has several problematic consequences and that it’s not obvious how the principle might be restricted in order (...) to avoid them. My suggestion is that, instead of trying to restrict the principle, we should distinguish between metaphysical and conceptual grounds and take the principle to apply exclusively to the latter. This suggestion, if correct, carries over to other prominent attempts at using logical form as a guide to ground. (shrink)

In this paper we study proof procedures for some variants of first-order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect to the variants of the considered logics. The treatment of each variant is equally simple and is based on the annotation of functional symbols by natural numbers, conveying some semantical information on the worlds (...) where they are meant to be interpreted.This paper is an extended version of a previous work where full proofs were not included. Proofs are in some points rather tricky and may help in understanding the reasons for some details in basic definitions. (shrink)

Applies the Conformal Framework to the philosophy of logic, and, in particular, to what McCarthy calls the Interpretation Problem for Logic, i.e. the problem of characterizing the logical devices of a language, as opposed to its descriptive expressions, paradigm examples of which include observational predicates and natural kind terms, on the basis of the data provided by an interpretation of its speakers. An extension of the Conformal Framework is given that facilitates a general solution to the interpretation problem: a (...) logical constant, on McCarthy's account, is an operator whose semantic role is invariant under structure‐preserving transformations defined across situations, which are epistemically possible for the idealized intentional system interpreted. Such a characterization results in a relative determinacy: the interpretations of the logical terms in the intentional system's language are fixed by the role they play in stories describing worlds that are epistemically possible for the system, which in turn is fixed by the system's inductive method. (shrink)

In Poggiolesi we have introduced a rigorous definition of the notion of complete and immediate formal grounding; in the present paper our aim is to construct a logic for the notion of complete and immediate formal grounding based on that definition. Our logic will have the form of a calculus of natural deduction, will be proved to be sound and complete and will allow us to have fine-grained grounding principles.

In ‘What on Earth is Logic?’, Michael Shenefelt and Heidi White offer this observation about the nature of logic: ‘If one tries to justify logic logically, one ends up arguing in a circle’. From this, they conclude that ‘logic is a horizon beyond which none of our earnest self-reflecting arguments can help us see’. While there is much to appreciate in how they developed this idea, there are several worrying points that could still be raised against their view. In this (...) article, we outline such problems.Export citation. (shrink)

This paper is concerned with the semantics for the logics of ground that derive from a slight variant GG of the logic of (Fine, 2012) that have already been developed in (deRosset and Fine, 2023). Our aim is to outline that semantics and to provide a comparison with two related semantics for ground, given in (Correia, 2017) and (Kraemer, 2018). This comparison highlights the strengths and difficulties of these different approaches.

I lay down a system of structural rules for various notions of ground and establish soundness and completeness.

We prove that for a natural class of first-order formulas the validity problem is Π p 2 -complete.

Every thinker is related to the history of thought, but investigating this relationship is not always interesting or even profitable. In the case of Hegel, however, the philosopher’s relationship to the history of thought is one of the chief things that recommends his philosophy as a subject of study. But what makes Hegel interesting also makes him difficult, for Hegel was acutely conscious of his relation to the tradition. Perhaps Hegel had a broader and deeper awareness of this relationship than (...) any thinker before him. But this is not the important thing. What matters is that Hegel seized upon his relationship to the tradition as a problem, translating it from the language of dim, circumstantial connections into the language of philosophy’s essential vocation. For Hegel, philosophy’s relationship to the tradition is not in the first place a fact about the system of thought. It is rather the logical destiny that rules its genesis, development and perfection. The determination to put the problem of this relationship on philosophy’s agenda and so make it scientifically profitable for raising thought to maturity is the heart and soul of Hegel’s preface to the Phenomenology of Spirit. This text celebrates phenomenological science as the “ladder” for leading consciousness upward into its true element, science, just at the moment when consciousness has been prepared by its historical experience to take this step. (shrink)

Modelling, reasoning and verifying complex situations involving a system of agents is crucial in all phases of the development of a number of safety-critical systems. In particular, it is of fundamental importance to have tools and techniques to reason about the doxastic and epistemic states of agents, to make sure that the agents behave as intended. In this paper we introduce a computationally grounded logic called COGWED and we present two types of semantics that support a range of practical situations. (...) We provide model checking algorithms, complexity characterisations and a prototype implementation. We validate our proposal against a case study from the avionic domain: we assess and verify the situational awareness of pilots flying an aircraft with several automated components in off-nominal conditions. (shrink)

An examination of the grounds of logical necessity is offered by taking its lead from Barry Stroud’s challenge to the possibility of articulating satisfactorily any such grounds in full generality. The intelligibility of logical aliens is also considered, and different conceptions of such aliens, some more radical in their treatment of the issue than others, are examined as well. Logical aliens are beings whose thinking goes beyond the limits of thought, presumably with a logic different from our (...) own. I argue that logical aliens are either something straightforward and unproblematic or something we cannot recognize as logical. In either case, there are ways of accommodating such aliens despite the fact that the search for grounds of logical necessity is ultimately misguided. (shrink)

The paper deals with the heuristic prerequisites of paraconsistent logic in the case of imaginary logic of N.A. Vasiliev proposed in 1910.

In this essay, I argue for a view that inclusive positivists share with Ronald Dworkin. According to the Moral Incorporation Thesis (MIT), it is logically possible for a legal system to incorporate moral criteria of legality (or “grounds of law,” as Dworkin puts it). Up to this point, the debate has taken the shape of attacks on the coherence of MIT with the defender of MIT merely attempting to refute the attacking argument. I give a positive argument for MIT. I (...) begin with an explanation of the logic of establishing possibility claims, such as MIT. At the outset, it is worth noting that the logic of establishing possibility claims is very different from the logic of establishing contingent descriptive claims or necessary claims. For this reason, some explication of the relevant features of the semantics of modal logic will be necessary here. Once the structural framework is adequately developed, the argument for MIT will be grounded on the strength of a thought experiment of a surprisingly simple kind. Indeed, the argument is inspired by a Razian argument for the possibility of a legal system without coercive enforcement machinery; on his view, a society of angels could still have a system of law without any coercive machinery. My argument will possess two theoretically important qualities that are also possessed by Raz’s powerfully simple, but ultimately unsuccessful, argument. (shrink)

Seeks to redraw the boundaries between the fields of geology and environmental philosophy.

The notion of belongingness in African philosophy has its most profound expression in Pantaleon Iroegbu’s uwa ontology, which stipulates that being is that which exists in the community, or, as he puts it, “To be is to belong.” The main contention of this article is that Jonathan O. Chimakonam’s ezumezu logic is fully equipped to explain this ontology of belongingness. This is due to the trivalent and dynamic nature of this African culture–inspired logic, which adequately captures the African conception of (...) reality. According to this conception, individual entities continue to coexist or to belong in the community without losing their respective identities. (shrink)

What corresponds to the present-day ‘transcendental-pragmatic’ concept of ultimate grounding in Hegel is his claim to absoluteness of the logic. Hegel’s fundamental intuition is that of a ‘backward going grounding’ obtaining the initially unproved presuppositions, thereby ‘wrapping itself into a circle’ – the project of the self-grounding of logic, understood as the self-explication of logic by logical means. Yet this is not about one of the multiple ‘logics’ which as formal constructs cannot claim absoluteness. It is rather a fundamental (...) logic that only makes logical textures possible at all and so owns transcendental character. The non-contradiction-principle is an example for this. Es- sential is that it is ‘under-cover-effcient’ as soon as meaningful concepts are used. Self-explication of the fundamental logic then means explicating its implicit under-cover validity, in fact by means of the fundamental logic itself. As is shown this is the affair of dialectic which thereby is to be understood as ultimate grounding of the fundamental logic. This is analyzed in detail using the example of the being/non-being-dialectic. As is demonstrated each explication step generates a new implicit issue and therewith a new explication-discrepancy inducing an antinomical structure that anew forwards the explication procedure. So this is entirely determined by itself. Decisive for the ultimate grounding argumentation is that thereby an objectively verifyable procedure is found, which is apparently possible only in a Hegelian framework. In contrast the immediate evidence of a speech act claimed by the transcendental-pragmatic position has only private character, which is grounding-theoretically irrelevant. (shrink)

This paper is a contribution to the long-standing debate over the coherence of Charles Sanders Peirce’s overall system of philosophy. It approaches that issue through the lens of a contemporary debate over the notion of metaphysical grounding, or more broadly, the nature of metaphysical explanation, employing the laws of logic as a case study. The central question concerns how we can take seriously what we shall call Peirce’s Rule—that nothing can be admitted to be absolutely inexplicable—without being vulnerable to a (...) vicious regress or equally vicious circularity. I first argue that in Peirce’s early work he offers a quietist conception of grounding that provides a persuasive and ground-breaking answer to this central question. I then raise a familiar concern, that in Peirce’s later work we find hints of a more metaphysical conception of grounding that seems unable to answer that question and is thus inconsistent with his earlier work. The paper ends with a speculative interpretation of Peirce’s approach to metaphysics and its possible role in grounding logical principles. (shrink)

Many efforts have been made in recent years to construct formal systems for mechanizing general mathematical reasoning. Most of these systems are based on logics which are stronger than first-order logic. However, there are good reasons to avoid using full second-order logic for this task. In this work we investigate a logic which is intermediate between FOL and SOL, and seems to be a particularly attractive alternative to both: ancestral logic. This is the logic which is obtained from FOL by (...) augmenting it with the transitive closure operator. While the study of this logic has so far been mostly model-theoretical, this work is devoted to its proof theory. Two natural Gentzen-style proof systems for ancestral logic are presented: one for the reflexive transitive closure, and one for the non-reflexive one. We show that these systems are sound for ancestral logic and provide evidence that they indeed encompass all forms of reasoning for this logic that are used in practice. The two systems are shown to be equivalent by providing translation algorithms between them. We end with an investigation of two main proof-theoretical properties: cut elimination and constructive consistency proof. (shrink)

We define the term \a set T of sentential-logical formulae grounds a sentential-logical formula A from a syntactic point of view\ in such a way that A is a syntactic sentential-logical consequence of T, and specific additional syntactic requirements regarding T and A are fulfilled. These additional requirements are developed strictly within the syntactics of sentential-logical languages, the three most important being new, namely: to be atomically minimal, to be minimal in degree, and not to be (...) conjunction-like. Our approach is independent of any specific sentential-logical calculus. (shrink)

I give a semantic characterisation of a system for the logic of grounding similar to the system introduced by Kit Fine in his “Guide to Ground”, as well as a semantic characterisation of a variant of that system which excludes the possibility of what Fine calls ‘zero-grounding’.

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces a number of (...) problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (shrink)