333,247 research outputs found
Global Numerical Constraints on Trees
We introduce a logical foundation to reason on tree structures with
constraints on the number of node occurrences. Related formalisms are limited
to express occurrence constraints on particular tree regions, as for instance
the children of a given node. By contrast, the logic introduced in the present
work can concisely express numerical bounds on any region, descendants or
ancestors for instance. We prove that the logic is decidable in single
exponential time even if the numerical constraints are in binary form. We also
illustrate the usage of the logic in the description of numerical constraints
on multi-directional path queries on XML documents. Furthermore, numerical
restrictions on regular languages (XML schemas) can also be concisely described
by the logic. This implies a characterization of decidable counting extensions
of XPath queries and XML schemas. Moreover, as the logic is closed under
negation, it can thus be used as an optimal reasoning framework for testing
emptiness, containment and equivalence
Propositional Logics Complexity and the Sub-Formula Property
In 1979 Richard Statman proved, using proof-theory, that the purely
implicational fragment of Intuitionistic Logic (M-imply) is PSPACE-complete. He
showed a polynomially bounded translation from full Intuitionistic
Propositional Logic into its implicational fragment. By the PSPACE-completeness
of S4, proved by Ladner, and the Goedel translation from S4 into Intuitionistic
Logic, the PSPACE- completeness of M-imply is drawn. The sub-formula principle
for a deductive system for a logic L states that whenever F1,...,Fk proves A,
there is a proof in which each formula occurrence is either a sub-formula of A
or of some of Fi. In this work we extend Statman result and show that any
propositional (possibly modal) structural logic satisfying a particular
formulation of the sub-formula principle is in PSPACE. If the logic includes
the minimal purely implicational logic then it is PSPACE-complete. As a
consequence, EXPTIME-complete propositional logics, such as PDL and the
common-knowledge epistemic logic with at least 2 agents satisfy this particular
sub-formula principle, if and only if, PSPACE=EXPTIME. We also show how our
technique can be used to prove that any finitely many-valued logic has the set
of its tautologies in PSPACE.Comment: In Proceedings DCM 2014, arXiv:1504.0192
Grounding the Lexical Semantics of Verbs in Visual Perception using Force Dynamics and Event Logic
This paper presents an implemented system for recognizing the occurrence of
events described by simple spatial-motion verbs in short image sequences. The
semantics of these verbs is specified with event-logic expressions that
describe changes in the state of force-dynamic relations between the
participants of the event. An efficient finite representation is introduced for
the infinite sets of intervals that occur when describing liquid and
semi-liquid events. Additionally, an efficient procedure using this
representation is presented for inferring occurrences of compound events,
described with event-logic expressions, from occurrences of primitive events.
Using force dynamics and event logic to specify the lexical semantics of events
allows the system to be more robust than prior systems based on motion profile
A PSYCHOLINGUISTIC ANALYSIS OF SCHIZOPHRENIC SPEECH REFLECTING HALLUCINATION AND DELUSION IN THE CAVEMAN’S VALENTINE
The objectives of this research are (1) to explain the speech abnormalities
of a schizophrenic character, Romulus, in The Caveman’s Valentine; and (2) to
present the characteristics of schizophrenia represented by Romulus in his speech.
This research employed a descriptive qualitative method. It was concerned
with the description of the data in the form of utterances produced by the
schizophrenic character, Romulus, in which the phenomena of schizophrenic
speech abnormalities exist. Quantification of the data was also done in this
research, only to strengthen the answer of the first objective. Meanwhile, for the
second objective, the explanation is without number. Finally, in order to support
the credibility of the data findings, data trustworthiness was maintained in the
form of triangulation and peer discussion (peer debriefing).
The findings of this research show that first, among the eight types of
schizophrenic speech abnormalities, only four of them occur. They are looseness,
perseveration of ideas, peculiar use of words, and non-logical reasoning (peculiar
logic). Looseness is the first most-often appearing phenomenon, followed by
perseveration of ideas, peculiar use of words, and non-logical reasoning (peculiar
logic). Second, all characteristics of schizophrenia, i.e. hallucination and delusion,
are also shown in the movie. Hallucination is represented by the occurrence of
visual and auditory hallucination, while delusion is represented by the occurrence
of paranoid delusion and delusion of reference. In addition, for the characteristics
of schizophrenia, the number of the occurrence of each phenomenon is not
important since the existence of each characteristic is enough to judge that
someone suffers from schizophrenia.
Keywords : schizophrenia, looseness, perseveration of ideas, peculiar use of
words, non-logical reasoning (peculiar logic), hallucination,
delusion, The Caveman’s Valentin
Uniform Substitution for Differential Game Logic
This paper presents a uniform substitution calculus for differential game
logic (dGL). Church's uniform substitutions substitute a term or formula for a
function or predicate symbol everywhere. After generalizing them to
differential game logic and allowing for the substitution of hybrid games for
game symbols, uniform substitutions make it possible to only use axioms instead
of axiom schemata, thereby substantially simplifying implementations. Instead
of subtle schema variables and soundness-critical side conditions on the
occurrence patterns of logical variables to restrict infinitely many axiom
schema instances to sound ones, the resulting axiomatization adopts only a
finite number of ordinary dGL formulas as axioms, which uniform substitutions
instantiate soundly. This paper proves soundness and completeness of uniform
substitutions for the monotone modal logic dGL. The resulting axiomatization
admits a straightforward modular implementation of dGL in theorem provers
A Uniform Substitution Calculus for Differential Dynamic Logic
This paper introduces a new proof calculus for differential dynamic logic
(dL) that is entirely based on uniform substitution, a proof rule that
substitutes a formula for a predicate symbol everywhere. Uniform substitutions
make it possible to rely on axioms rather than axiom schemata, substantially
simplifying implementations. Instead of nontrivial schema variables and
soundness-critical side conditions on the occurrence patterns of variables, the
resulting calculus adopts only a finite number of ordinary dL formulas as
axioms. The static semantics of differential dynamic logic is captured
exclusively in uniform substitutions and bound variable renamings as opposed to
being spread in delicate ways across the prover implementation. In addition to
sound uniform substitutions, this paper introduces differential forms for
differential dynamic logic that make it possible to internalize differential
invariants, differential substitutions, and derivations as first-class axioms
in dL
Ancient Indian Logic and Analogy
B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic
- …