1,753 research outputs found
Linear Temporal Logic and Propositional Schemata, Back and Forth
Session: p-Automata and Obligation Games - http://www.isp.uni-luebeck.de/time11/International audienceThis paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced in elsewhere by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one logic to the other. Some consequences about complexity are given. We report about first experiments and the consequences about possible improvements in existing implementations are analyzed
Linear Temporal Logic and Propositional Schemata, Back and Forth (extended version)
This paper relates the well-known Linear Temporal Logic with the logic of
propositional schemata introduced by the authors. We prove that LTL is
equivalent to a class of schemata in the sense that polynomial-time reductions
exist from one logic to the other. Some consequences about complexity are
given. We report about first experiments and the consequences about possible
improvements in existing implementations are analyzed.Comment: Extended version of a paper submitted at TIME 2011: contains proofs,
additional examples & figures, additional comparison between classical
LTL/schemata algorithms up to the provided translations, and an example of
how to do model checking with schemata; 36 pages, 8 figure
Integrating a Global Induction Mechanism into a Sequent Calculus
Most interesting proofs in mathematics contain an inductive argument which
requires an extension of the LK-calculus to formalize. The most commonly used
calculi for induction contain a separate rule or axiom which reduces the valid
proof theoretic properties of the calculus. To the best of our knowledge, there
are no such calculi which allow cut-elimination to a normal form with the
subformula property, i.e. every formula occurring in the proof is a subformula
of the end sequent. Proof schemata are a variant of LK-proofs able to simulate
induction by linking proofs together. There exists a schematic normal form
which has comparable proof theoretic behaviour to normal forms with the
subformula property. However, a calculus for the construction of proof schemata
does not exist. In this paper, we introduce a calculus for proof schemata and
prove soundness and completeness with respect to a fragment of the inductive
arguments formalizable in Peano arithmetic.Comment: 16 page
From Mirror to Mirage: The Idea of Logical Space in Kant, Wittgenstein, and van Fraassen
This dissertation investigates the origin, intellectual development and use of a semantic variant of the idea of logical space found implicitly in Kant and explicitly in early Wittgenstein and van Fraassen. It elucidates the idea of logical space as the idea of images or pictures representative of reality organized into a logico-mathematical structure circumscribing a form of all possible worlds. Its main claim is that application of these images or pictures to reality is through a certain conception of self.
The first chapter presents a novel interpretation of Kant’s semantic theory of schemata in the Critique of Pure Reason, showing that a structure of the imagination induced by the transcendental self informs an implicit idea of logical space. The second chapter offers an intellectual history of the idea through developments in the organization of images introduced by Helmholtz and Hertz. The third chapter reveals early Wittgenstein’s idea of logical space to be his notion of the self, demonstrating how this serves to unify propositions of the Tractatus Logico-Philosophicus concerning solipsism, realism, ethics, aesthetics and mysticism with those pertaining to the picture theory of meaning. The fourth chapter provides a historical overview of the development of van Fraassen’s empiricism in relation to his adaptation of logical space, and evaluates his recent proposal in Scientific Representation: Paradoxes of Perspective that the problem of coordination in the semantic view of theories is dissolved through self-location in logical space. After identifying a number of problems this proposal creates for his empiricism, a brief suggestion is made about how van Fraassen might improve upon his conception of logical space, and how an empiricist view of scientific representation might be understood as a result
State-of-the-art on evolution and reactivity
This report starts by, in Chapter 1, outlining aspects of querying and updating resources on
the Web and on the Semantic Web, including the development of query and update languages
to be carried out within the Rewerse project.
From this outline, it becomes clear that several existing research areas and topics are of
interest for this work in Rewerse. In the remainder of this report we further present state of
the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give
an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs;
in Chapter 4 event-condition-action rules, both in the context of active database systems and
in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks
Ancient Logic and its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972
Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others.
Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic
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Modeling Narrative Discourse
This thesis describes new approaches to the formal modeling of narrative discourse. Although narratives of all kinds are ubiquitous in daily life, contemporary text processing techniques typically do not leverage the aspects that separate narrative from expository discourse. We describe two approaches to the problem. The first approach considers the conversational networks to be found in literary fiction as a key aspect of discourse coherence; by isolating and analyzing these networks, we are able to comment on longstanding literary theories. The second approach proposes a new set of discourse relations that are specific to narrative. By focusing on certain key aspects, such as agentive characters, goals, plans, beliefs, and time, these relations represent a theory-of-mind interpretation of a text. We show that these discourse relations are expressive, formal, robust, and through the use of a software system, amenable to corpus collection projects through the use of trained annotators. We have procured and released a collection of over 100 encodings, covering a set of fables as well as longer texts including literary fiction and epic poetry. We are able to inferentially find similarities and analogies between encoded stories based on the proposed relations, and an evaluation of this technique shows that human raters prefer such a measure of similarity to a more traditional one based on the semantic distances between story propositions
Mental content : consequences of the embodied mind paradigm
The central difference between objectivist cognitivist semantics and embodied cognition consists in the fact that the latter is, in contrast to the former, mindful of binding meaning to context-sensitive mental systems. According to Lakoff/Johnson's experientialism, conceptual structures arise from preconceptual kinesthetic image-schematic and basic-level structures. Gallese and Lakoff introduced the notion of exploiting sensorimotor structures for higherlevel cognition. Three different types of X-schemas realise three types of environmentally embedded simulation: Areas that control movements in peri-personal space; canonical neurons of the ventral premotor cortex that fire when a graspable object is represented; the firing of mirror neurons while perceiving certain movements of conspecifics. ..
Software tools for the cognitive development of autonomous robots
Robotic systems are evolving towards higher degrees of autonomy. This paper reviews the cognitive tools available nowadays for the fulfilment of abstract or long-term goals as well as for learning and modifying their behaviour.Peer ReviewedPostprint (author's final draft
A semantic theory of a subset of qualifying "as" phrases in English
Landman (1989) introduced contemporary linguistics to the as-phrase. An as-phrase
is a qualifier, introduced in English by "as." "John is corrupt as a judge," for instance,
contains the as-phrase "as a judge." Philosophical discourse is full of examples of
as-phrase sentences. Their presence can make it difficult to distinguish valid from
invalid arguments, a perennial concern for philosophers. Landman proposed the first
formal semantic theory of as-phrases, based on a set of seven intuitively-valid patterns
of inference involving as-phrases. SzabĂł (2003), Jaeger (2003), Asher (2011) each
attempt to improve upon Landman's theory.
Chapter 1 reviews and criticizes a temporal account of as-phrase semantics,
while tracing some precedents and motivations for my approach. Chapters 2-3 criticize
SzabĂł's and Asher's theories. SzabĂł's theory shows problems handling the future
tense and intensional contexts. Asher's complex theory solves these problems, but
resorts to the obscure notions of relative identity and bare particulars.
Chapter 4 argues that neither SzabĂł's nor Asher's theory is clearly superior, because
implicitly, they focus on different classes of sentences, which I call "Type A" and
"Type B." From John Bowers' syntactic research, I argue that the element common
to Type A and Type B is Pr, a predication head pronounced "as" in some contexts.
Chapter 5 develops a formal semantic theory tailored to Type A sentences that solves
the problems of SzabĂł's theory while avoiding Asher's assumptions. On my approach,
the semantic properties of Type A sentences resolve into an interaction among generic
quantifiers, determiner-phrase interpretation, and one core quantifier based on a principal
ultrafilter. It is the interaction-effects of these elements that give rise to the many
unusual readings we find in these as-phrase sentences. This result supports my motivating
view that linguistic research helps to solve semantic problems of philosophical
interest
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