Entailment Principle Research Articles

Psychophysiological approach to the Liar paradox: Jean Buridan’s virtual entailment principle put to the test

This article presents an empirical examination of the consequences of the virtual entailment principle proposed by Jean Buridan to resolve the Liar paradox. This principle states that every sentence in natural language implicitly asserts its own truth. Adopting this principle means that the Liar sentence is not paradoxical but false, because its content is contradictory to what is virtually implied. As a result, humans should perceive the Liar sentence the same way as any other false sentence. This solution to the Liar paradox received criticism for making ad hoc claims about the natural language. However, thanks to modern advancements in psychophysiology, it became possible to empirically investigate if the human brain really perceives the Liar sentence like a false sentence. We designed and conducted an experiment to examine brain activity in response to true sentences, false sentences and self-referential sentences (including the Liar and the Truthteller). Our results provide support for the Buridan’s hypothesis and show that the Liar sentence is processed by the human brain identically to false sentences, while the Truthteller sentence is perceived identically to true sentences. This agrees with predictions derived from the virtual entailment principle and supports the idea that humans think with the logic of truth—a logic for which the truth is a designated value of its adequate semantics.

Grounding entails supervenience

Do grounding claims entail corresponding supervenience claims? The question matters, as a positive answer would help grounding theorists address worries that their hyperintensional primitive is obscure, and also increase the argumentative strategies that are available within ground-theoretic frameworks for metaphysical inquiry. Leuenberger (Erkenntnis 79:227–240, 2014a) argues for a negative response, by specifying some candidate principles of entailment and then claiming that each of them is subject to counterexamples. In this paper, I critically assess those principles and the objections he raises against them, and advocate a novel entailment principle that overcomes all the problems suffered by those other principles. The principle I defend places a supervenience-based constraint on grounding claims, and secures a substantive connection between grounding and modality, weaker than necessitation.

Causal grounds for negative truths

Among truthmaker theorists it is generally thought that we are not able to use the entailment principle (i.e. the principle according to which truthmaking distributes across entailment) to ground negative truths. But these theorists usually only discuss truthmakers for truth-functional complexes, thereby overlooking the fact that there are non-truth-functional complexes whose truth values are not solely determined by the truth or falsity of their atomic propositions. And once we expand the class of truths that require their own bespoke truthmakers to also include these, there is no reason to exempt negative truths from grounding. For given that truthmaking is closed under entailment and every negative truths is entailed by some non-truth-functional complex or other, any resources rich enough to ground the truth of the latter will do the same job for the former.

Do we need a new theory of truthmaking? Some comments on Disjunction Thesis, Conjunction Thesis, Entailment Principle and explanation

In the paper we discuss criticisms against David Armstrong’s general theory of truthmaking by Gonzalo Rodriguez-Pereyra, Peter Schulte and Benjamin Schnieder, and conclude that Armstrong’s theory survives these criticisms. Special attention is given to the problems concerning Entailment Principle, Conjunction Thesis, Disjunction Thesis and to the notion of explanation.

Entailment Principle for Measure-Based Uncertainty

We describe the use of monotonic set measures, which are sometimes referred to as fuzzy measures, in the representation of uncertain information about a variable. The representation of significant types of uncertain information, such as probabilistic, possibilistic, and others, is discussed. The concept of the dual of a measure is introduced and is used to define the measures of opportunity and assurance associated with the occurrence of an event. We observe that these generalize the ideas of possibility and necessity in possibility theory, as well as the ideas of plausibility and belief in Dempster-Shafer theory. Using the measures of opportunity and assurance, we are able to introduce a concept of entailment between two uncertainty representations, which generalizes Zadeh's idea of entailment between possibility distributions. We show, using the idea of entailment, how to relate possibilistic and probabilistic uncertainty and discuss a potential application in hard/soft information fusion. We, finally, consider the measure representation of joint variables.

On Possibilistic and Probabilistic Information Fusion

This article discusses the basic features of information provided in terms of possibilistic uncertainty. It points out the entailment principle, a tool that allows one to infer less specific from a given piece of information. The problem of fusing multiple pieces of possibilistic information is and the basic features of probabilistic information are described. The authors detail a procedure for transforming information between possibilistic and probabilistic representations, and using this to form the basis for a technique for fusing multiple pieces of uncertain information, some of which is possibilistic and some probabilistic. A procedure is provided for addressing the problems that arise when the information to be fused has some conflicts.

Reasoning with doubly uncertain soft constraints

We describe the basic ideas of the theory of approximate reasoning and indicate how it provides a framework for representing human sourced soft information. We discuss how to translate linguistic knowledge into formal representations using generalized constraints. We consider the inference process within the theory of approximate reasoning and introduce the entailment principle and describe its centrality to this inference process. Next we introduce the idea of doubly uncertain statements such as John’s friend is young. In these statements there exists uncertainty both with respect to value of the age, young, and the object associated with the age, John’s friend. We suggest a method for representing these complex statements and investigate the problem of making inferences about specific objects.

The Disjunction and Conjunction Theses

This paper is a response to replies by Dan López de Sa and Mark Jago to my ‘Truthmaking, Entailment, and the Conjuction Thesis’. In that paper, my main aim was to argue against the Entailment Principle by arguing against the Conjunction Thesis, which is entailed by the Entailment Principle. In the course of so doing, although not essential for my project in that paper, I defended the Disjunction Thesis. López de Sa has objected both to my defence of the Disjunction Thesis and my case against the Conjunction Thesis. I shall show that his objections are unfounded and based on serious misunderstandings of my position, what the relevant debate is, and some fundamental notions of Truthmaker Theory. Jago argues that accepting the Disjunction Thesis and rejecting the Conjunction Thesis is hard to maintain. But I show that Jago has not shown that accepting the Disjunction Thesis while rejecting the Conjunction Thesis is impossible or even hard to maintain. Jago believes that, to accept the Disjunction Thesis while rejecting the Conjunction Thesis, one needs to reject his axiom (T3), which says that all the truthmakers for 〈P&P〉 are truthmakers for 〈P〉. I argue that there are reasons to reject such a principle, and the version of it that says that what makes 〈P&P〉 true makes 〈P〉 true.

Entropy conserving probability transforms and the entailment principle

Our main result here is the development of a general procedure for transforming some initial probability distribution into a new probability distribution in a way that the resulting distribution has entropy at least as great as the original distribution.A significant aspect of our approach is that it makes use of Zadeh's entailment principle which is itself a general procedure for going from an initial possibility distribution to a new possibility distribution so that the resulting possibility has an uncertainty at least as great as the original.

Truthmaking, Entailment, and the Conjunction Thesis

In this paper I undermine the Entailment Principle according to which if an entity is a truthmaker for a certain proposition and this proposition entails another, then the entity in question is a truthmaker for the latter proposition. I argue that the two most promising versions of the principle entail the popular but false Conjunction Thesis, namely that a truthmaker for a conjunction is a truthmaker for its conjuncts. One promising version of the principle understands entailment as strict implication but restricts the field of application of the principle to purely contingent truths (i.e. those that contain no necessary proposition at any level of analysis). But a conjunction of purely contingent truths strictly implies its conjuncts. So this version of the principle is committed to the Conjunction Thesis. The same is true of the version of the principle where entailment is understood in the sense of systems T, R, and E of relevant logic, since in these systems conjunctions entail their conjuncts. I argue that the Conjunction Thesis is false because a truthmaker is that in virtue of what a certain proposition is true and it is false that, for example, what the proposition that Peter is a man is true in virtue of is the conjunctive fact that Peter is man and Saturn is a planet (or the facts that Peter is a man and that Saturn is a planet taken together). I also argue against other versions of the principle.

Nonmonotonic reasoning: from complexity to algorithms

The purpose of this paper is to outline various results regarding the computational complexity and the algorithms of nonmonotonic entailment in different coherence‐based approaches. Starting from a (non necessarily consistent) belief base E and a pre‐order on E, we first present different mechanisms for selecting preferred consistent subsets. Then we present different entailment principles in order to manage these multiple subsets. The crossing point of each generation mechanism m and each entailment principle p defines an entailment relation $$ (E, \leqslant )\left| \sim \right.^{p,m} \Phi $$ which we study from the computational complexity point of view. The results are not very encouraging since the complexity of all these nonmonotonic entailment relations is, in most restricted languages, larger than the complexity of monotonic entailment. So, we decided to extend Binary Decision Diagrams technics, which are well suited to the task of solving NP‐hard logic‐based problems. Both theoretical and experimental results are described along this line in the last sections.

How to be a Fallibilist

The acceptance of fallibilism in epistemology is virtually universal. Any theory of knowledge that endorses the principle that S knows q on the basis of reason r only if r entails q, is doomed to a skeptical conclusion. Fallibilist theories reject this entailment principle thereby avoiding this immediate skeptical result. The acceptance of fallibilism derives from the widely held view that what we seek in constructing a theory of knowledge is an account that squares with our strong intuition that we know many things. Of course, few believe that skepticism is to be avoided at all costs. But while the entailment principle may look attractive in the abstract, it does not command the kind of assent sufficient to withstand the overwhelming case against it provided by our everyday intuitions concerning what we know. Any residual worry associated with denying the principle is far outweighed by our common sense rejection of its skeptical consequences. Thus, a fallibilist theory allows that S can know q on the basis of r where r only makes q probable. Unfortunately, skepticism is not so easily dispatched. Other principles that look very difficult to reject threaten to reinstate skepticism-principles that lead to skeptical paradoxes for fallibilist theories. Thus, even fallibilist theories of knowledge are forced to confront skepticism, albeit in the form of a stubborn paradox rather than as a seemingly inescapable result. The theory of relevant alternatives can be viewed as providing fallibilist theories with a way out of skeptical paradoxes.' However, while the theory looks promising in its broad outline, many believe

The entailment principle for dempster—shafer granules

We discuss the rule of inference called the entailment principle which plays a significant role in the possibilistic type reasoning used in the theory of approximate reasoning. We extend this principle to situations in which the knowledge is a type of combination of possibilistic and probabilistic information which we call Dempster—Shafer granules. We discuss the conjunction of these D—S granules and show that Dempster's rule of combination is a special application of conjunction followed by a particular implementation of the entailment principle.