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Papers by Patrick Blackburn

Since the early 1990s, the semanticist Reinhard Muskens has advocated the use of the TYn family o... more Since the early 1990s, the semanticist Reinhard Muskens has advocated the use of the TYn family of higher-order logics as a general framework for semantic representation; he has backed up his claim by treating a wide variety of semantic phenomena in the TYn framework. Most interestingly of all, he has also shown that the central ideas of Discourse Representation Theory (DRT) can be modeled in TYn, thereby allowing a clean Montague-style treatment of discourse level phenomena. In this paper, we assess the significance for ...

Advances in Modal Logic, 2016

Hybrid logic is a form of modal logic which allows reference to worlds. We can think of it as 'mo... more Hybrid logic is a form of modal logic which allows reference to worlds. We can think of it as 'modal logic with labelling built into the object language' and various forms of labelled deduction have played a central role in its proof theory. Jerry Seligman's work [13,14] in which 'rules involving labels' are rejected in favour of 'rules for all' is an interesting exception to this. Seligman's approach was originally for natural deduction; the authors of the present paper recently extended it to tableau inference [1,2]. Our earlier work was syntactic: we showed completeness by translating between Seligman-style and labelled tableaus, but our results only covered the minimal hybrid logic; in the present paper we provide completeness results for a wider range of hybrid logics and languages. We do so by adapting the synthetic approach to tableau completeness (due to Smullyan, and widely applied in modal logic by Fitting) so that we can directly build maximal consistent sets of tableau blocks.

Electronic Proceedings in Theoretical Computer Science

We describe a natural deduction formalization of intuitionistic and classical propositional logic... more We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to logical modelling, here we employ a logical framework modelling. This gives rise to simple and natural teaching examples and we report on the role it played in teaching our Automated Reasoning course in 2020 and 2021.

A.N. Prior (1914-69) in the course of the 1950s and 1960s founded a new and revolutionary paradig... more A.N. Prior (1914-69) in the course of the 1950s and 1960s founded a new and revolutionary paradigm in philosophy and logic. Its most central feature is the preoccupation with time and the development of the logic of time. However, this was inseparably interwoven with fundamental questions about human freedom, ethics, and existence. This remarkable integration of themes also embodies an original and in fact revolutionary conception of logic. The book series, Logic and Philosophy of Time, is dedicated to a deep investigation and also the further development of Prior's paradigm.

This paper argues that A.N. Prior’s invention of tense-logic constitutes a return of medieval log... more This paper argues that A.N. Prior’s invention of tense-logic constitutes a return of medieval logic in the philosophy of time. The argument proceeds from an analysis of W.V. Quine and P.W. Strawson’s 1953 discussion about the inability of formal logic to analyse the tenses of ordinary language. Recent discoveries in the A.N. Prior archive at the Bodleian Library in Oxford reveal that J.J.C. Smart, in a letter to Prior, brought up their discussion in his rejection of Prior’s invention of tense-logic. The correspondence will be discussed in terms of the importance of Prior’s discovery of tense-logic and the presentation of this as a solution to the problem discussed by Strawson and Quine in The Syntax of Time Distinctions (1958, [9]). Recent discoveries reveal a close connection between this discussion and Prior’s discussion of future contingency in Diodoran Modality (1955, [7]). These discoveries support the conclusion of this paper, which argues that Quine’s insistence that modern l...

This special issue of the Bulletin of the Section of Logic contains five papers, which were origi... more This special issue of the Bulletin of the Section of Logic contains five papers, which were originally presented at the Formal Methods and Science in Philosophy III conference, which was held at the Inter-University Centre, Dubrovnik, Croatia, 11–13 April 2019. The two previous editions of this meetings were held at the same location in 2015 and 2017, and as the third call for papers made clear, the Dubrovnik meeting again emphasized:

Journal of Logic, Language and Information, Oct 1, 2000

His [Turing's] point was that we should not be species-chauvinistic, or anthropocentric, about th... more His [Turing's] point was that we should not be species-chauvinistic, or anthropocentric, about the insides of an intelligent being, for there might be inhuman ways of being intelligent.

Lecture Notes in Computer Science, 2016

We first give a coarse-grained modal-logical analysis of the four best known second-order false-b... more We first give a coarse-grained modal-logical analysis of the four best known second-order false-belief tasks. This preliminary analysis shows that the four tasks share a common logical structure in which a crucial role is played by a "principle of inertia" which says that an agent's belief is preserved over time unless the agent gets information to the contrary. It also reveals informational symmetries (all four possibilities inherent in the two dimensions of deception versus no-deception and change-in-world versus change-in-belief-only are realized) and reveals a rather puzzling feature common to all four tasks. We then take a closer look at how the principle of inertia is used, which leads to a fine-grained analysis in terms of perspective shifting. We formalize this analysis using a natural deduction system for hybrid logic, and show that the proof modelling the solution to the first-order Sally-Anne task is nested inside the proof modelling the second-order solution.

THEORIA

In this article we discuss what constitutes a good choice of semantic representation, compare dif... more In this article we discuss what constitutes a good choice of semantic representation, compare different approaches of constructing semantic representations for fragments of natural language, and give an overview of recent methods for employing inference engines for natural language understanding tasks.

9th Indian Conference on Logic and its Applications, 2021

In a state-based modal logic, formulas are interpreted with respect to sets of possible worlds ra... more In a state-based modal logic, formulas are interpreted with respect to sets of possible worlds rather than individual worlds. In my talk I will present a bilateral version of a state-based modal logic motivated by linguistic phenomena at the semantics-pragmatics interface, including phenomena of free choice. In free choice inferences conjunctive meanings are derived from disjunctive sentences contrary to the prescriptions of classical logic: You may eat pizza or pasta =⇒ You may eat pizza and you may eat pasta Free choice inferences present a challenge to the canonical divide between semantics and pragmatics. They are not validities in classical modal logic and although they are derivable by conversational principles, they lack other characteristic properties of canonical pragmatic inferences, they are often non-cancellable, they are sometimes embeddable and their processing time has been shown to equal that of literal interpretations. In my bilateral state-based modal logic free choice and related inferences are derived by allowing pragmatic principles intrude in the recursive process of meaning composition. Contrary to most existing accounts where free choice inferences are viewed as special cases of quantity implicatures, the relevant pragmatic principle in our logic-based approach will be a version of Grice's Maxim of Quality.

Journal of Logic, Language and Information

This volume contains extended versions of six papers presented at the Seventh International Confe... more This volume contains extended versions of six papers presented at the Seventh International Conference on Logic, Rationality and Interaction (LORI-VII), which took place at SouthWest University in Chongqing (China) from October 18 to October 21, 2019 (for the complete conference proceedings, see Blackburn et al. 2019). The aim of the LORI conference series is to strengthen the interface between logic, epistemology, game theory, and social theory using perspectives drawn from philosophy, computer science, and artificial intelligence. Its topics of interest include (but are not limited to) epistemic logic, logic of/for games, computational social choice, logic of preference, deontic logic, logic of agency, conditional logic, logic and natural language, and argumentation theory. The papers included in this special issue all put special emphasis on "logic and interaction" and together offer a broad overview of ongoing research on this topic in both philosophy and in computer science. The papers address a number of themes, including the dynamics of distributed knowledge in multi-agent systems, strategic reasoning of rational agents in concurrent games, the formation of friendship and enmity relations in social networks, the connection between logic and supervised learning, the logical theory of causality, and the logic of knowledge and belief. To give a little more detail, the six selected papers are as follows: Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power by Thomas Ågotnes, Natasha Alechina, and Rustam Galimullin. This paper extends group announcement logic (GAL) by allowing quantification over announcements made by agents. Intuitively, such announcements (which may be joint) are related to the notion of distributed knowledge. Surprisingly, however, the paper shows that there are no interaction properties between GAL operators and distributed knowledge. The paper also investigates a number of other variants of GAL.

Aalborg Universitetsforlag, 2020

A.N. Prior developed his famous tense-logical paradigm during a period of 15 years (1954-1969). H... more A.N. Prior developed his famous tense-logical paradigm during a period of 15 years (1954-1969). However, it turns out that this work was done under the influence of a long struggle with scientific, philosophical and theological problems regarding time and reality. During his childhood, it was generally taken for granted that we can to some extent make free choices. However, when Prior was16 years old he wrote three booklets in which he rejected free-will and defended a kind of determinism related to the Calvinistic doctrine of predestination. He held on to this view for almost two decades, although he went through periods of doubt during which he felt that his world-view was challenged. In 1954 he finally left determinism and embraced a tense-logical account of indeterminism, presentism and change. In terms of McTaggart's A-and B-series this means that Prior as a teenager left the A-theoretical approach to time and reality which had dominated his childhood, and furthermore that after several years as a B-theorist he returned to a logically elaborated A-theory of time and reality. Prior's long metaphysical journey made it possible for him to suggest a tense-logical paradigm that reaches far beyond his own models and theories.

IfColog journal of logics and their applications (FLAP), 2017

Pinchinat & Schwarzentruber 8. John Slaney. Logic considered fun 9. Jeremy Seligman and Declan Th... more Pinchinat & Schwarzentruber 8. John Slaney. Logic considered fun 9. Jeremy Seligman and Declan Thompson. Teaching natural deduction in the right order with Natural Deduction Planner The contributions can be typed according to two main streams that are not exclusive:

Seventy-five years after the novel The Hobbit was published, the first part of its film adaptatio... more Seventy-five years after the novel The Hobbit was published, the first part of its film adaptation, The Hobbit: An Unexpected Journey, appeared in cinemas. The film trilogy (the second and third parts entitled The Hobbit: The Desolation of Smaug, and The Hobbit: The Battle of the Five Armies respectively) differs from the novel in a number of aspects, one of which is its onomastic stratum. The main aim of this article is to analyse the functions served by the characters' proper names in the novel and in the film trilogy and to compare these functions. The examination is based on the naming act in the novel, on the basis of which eight relations a name can enter into and thirteen roles it can serve have been identified.

9th Indian Conference on Logic and its Applications (Online), 2021

Journal of Logic, Language and Information, 2004

This paper discusses inference in computational semantics. We argue that state-of-the-art methods... more This paper discusses inference in computational semantics. We argue that state-of-the-art methods in first-order theorem proving and model generation are of direct relevance to inference for natural language processing. We support our claim by discussing our implementation of van der Sandt's presupposition projection algorithm in Discourse Representation Theory, an approach which demands sustained use of powerful inference mechanisms.

Journal of Logic and Computation, 2015

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Proceedings of 6th Workshop on Logic, …, 1999

The time evolution of the average spectral wave-action density, nk, of an ensemble of weakly inte... more The time evolution of the average spectral wave-action density, nk, of an ensemble of weakly interacting dispersive waves is governed by the so-called kinetic equation. For a system with dispersion law ωk, dominated by 3-wave interactions with interaction coefficient Lkk1k2, the kinetic equation is:∂ nk∂ t= 4π∫| Lkk1k2| 2 nknk1 nk2 F3 [n] δ (k− k1− k2) dk1dk2(1) where

Mathematics of Language, Jun 1, 2003

ABSTRACT. In this paper we examine three modal languages that have been proposed in the model the... more ABSTRACT. In this paper we examine three modal languages that have been proposed in the model theoretic syntax literature for describing finite ordered trees. We compare their expressive power, and then examine a key complexity-theoretic issue: how expensive it is to decide—given a theory specifying a certain class of trees—whether a formula describes a model? Our main result is that for the languages proposed by Blackburn et al. and Palm this problem is EXPTIME-complete.

Proc. of the 2003 …, 2003

The phase diagram of nuclear matter is quite rich-it shows such phenomena as phase-transitions, f... more The phase diagram of nuclear matter is quite rich-it shows such phenomena as phase-transitions, formation of condensates, clustering, etc. From the analysis of the spinodal instability, one can learn about the region of liquid-gas coexistence in nuclear matter at low densities and finite isospin asymmetries. In a recent paper, we have shown that asymmetric nuclear matter at sub-nuclear densities should undergo only one type of instability. The associated order parameter is dominated by the isoscalar density and so ...