Invariant-free deduction systems for temporal logic

In this thesis we propose a new approach to deduction methods for temporal logic. Our proposal is based on an inductive definition of eventualities that is different from the usual one. On the basis of this non-customary inductive definition for eventualities, we first provide dual systems of tableaux and sequents for Propositional Linear-time Temporal Logic (PLTL). Then, we adapt the deductive approach introduced by means of these dual tableau and sequent systems to the resolution framework and we present a clausal temporal resolution method for PLTL. Finally, we make use of this new clausal temporal resolution method for establishing logical foundations for declarative temporal logic programming languages. The key element in the deduction systems for temporal logic is to deal with eventualities and hidden invariants that may prevent the fulfillment of eventualities. Different ways of addressing this issue can be found in the works on deduction systems for temporal logic. Traditional tableau systems for temporal logic generate an auxiliary graph in a first pass.Then, in a second pass, unsatisfiable nodes are pruned. In particular, the second pass must check whether the eventualities are fulfilled. The one-pass tableau calculus introduced by S. Schwendimann requires an additional handling of information in order to detect cyclic branches that contain unfulfilled eventualities. Regarding traditional sequent calculi for temporal logic, the issue of eventualities and hidden invariants is tackled by making use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automation. A remarkable consequence of using either a two-pass approach based on auxiliary graphs or aone-pass approach that requires an additional handling of information in the tableau framework, and either invariant-based rules or infinitary rules in the sequent framework, is that temporal logic fails to carry out the classical correspondence between tableaux and sequents. In this thesis, we first provide a one-pass tableau method TTM that instead of a graph obtains a cyclic tree to decide whether a set of PLTL-formulas is satisfiable. In TTM tableaux are classical-like. For unsatisfiable sets of formulas, TTM produces tableaux whose leaves contain a formula and its negation. In the case of satisfiable sets of formulas, TTM builds tableaux where each fully expanded open branch characterizes a collection of models for the set of formulas in the root. The tableau method TTM is complete and yields a decision procedure for PLTL. This tableau method is directly associated to a one-sided sequent calculus called TTC. Since TTM is free from all the structural rules that hinder the mechanization of deduction, e.g. weakening and contraction, then the resulting sequent calculus TTC is also free from this kind of structural rules. In particular, TTC is free of any kind of cut, including invariant-based cut. From the deduction system TTC, we obtain a two-sided sequent calculus GTC that preserves all these good freeness properties and is finitary, sound and complete for PLTL. Therefore, we show that the classical correspondence between tableaux and sequent calculi can be extended to temporal logic. The most fruitful approach in the literature on resolution methods for temporal logic, which was started with the seminal paper of M. Fisher, deals with PLTL and requires to generate invariants for performing resolution on eventualities. In this thesis, we present a new approach to resolution for PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Our method is based on the dual methods of tableaux and sequents for PLTL mentioned above. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called TRS-resolution, that extends classical propositional resolution. Finally, we prove that TRS-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL. In the field of temporal logic programming, the declarative proposals that provide a completeness result do not allow eventualities, whereas the proposals that follow the imperative future approach either restrict the use of eventualities or deal with them by calculating an upper bound based on the small model property for PLTL. In the latter, when the length of a derivation reaches the upper bound, the derivation is given up and backtracking is used to try another possible derivation. In this thesis we present a declarative propositional temporal logic programming language, called TeDiLog, that is a combination of the temporal and disjunctive paradigms in Logic Programming. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. Since TeDiLog is, syntactically, a sublanguage of PLTL, the logical semantics of TeDiLog is supported by PLTL logical consequence. The operational semantics of TeDiLog is based on TRS-resolution. TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logic programming language that achieves this high degree of expressiveness. Since the tableau method presented in this thesis is able to detect that the fulfillment of an eventuality is prevented by a hidden invariant without checking for it by means of an extra process, since our finitary sequent calculi do not include invariant-based rules and since our resolution method dispenses with invariant generation, we say that our deduction methods are invariant-free.

Monodic Temporal Resolution

First-order temporal logic is a coincise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics have identified important enumerable and even decidable fragments. In this paper we present the first resolution-based calculus for monodic first-order temporal logic. Although the main focus of the paper is on establishing completeness result, we also consider implementation issues and define a basic loop-search algorithm that may be used to guide the temporal resolution system.

Temporal construal in advertising : the moderating role of temporal orientation and attribute importance in consumer evaluations

In two experiments, we study how the temporal orientation of consumers (i.e., future-oriented or present-oriented), temporal construal (distant future, near future), and product attribute importance (primary, secondary) influence advertisement evaluations. Data suggest that future-oriented consumers react most favorably to ads that feature a product to be released in the distant future and that highlight primary product attributes. In contrast, present-oriented consumers prefer near-future ads that highlight secondary product attributes. Study 2 shows that consumer attitudes are mediated by perceptions of attribute diagnosticity (i.e., the perceived usefulness of the attribute information). Together, these experiments shed light on how individual differences, such as temporal orientation, offer valuable insights into temporal construal effects in advertising.

A 1H-MRS investigation of the medial temporal lobe in antipsychotic-naïve and early-treated first episode psychosis

Schizophrenia is associated with significant brain abnormalities, including changes in brain metabolites as measured by proton magnetic resonance spectroscopy (MRS). What remains unclear is the extent to which these changes are a consequence of the emergence of psychotic disorders or the result of treatment with antipsychotic medication. We assessed 34 patients with first episode psychosis (15 antipsychotic naïve) and 19 age- and gender-matched controls using short-echo MRS in the medial temporal lobe bilaterally. Overall, there were no differences in any metabolite, regardless of treatment status. However, when the analysis was limited to patients with a diagnosis of schizophrenia, schizophreniform or schizoaffective disorder, significant elevations of creatine/phosphocreatine (Cr/PCr) and myo-inositol (mI) were found in the treated group. These data indicate a relative absence of temporal lobe metabolic abnormalities in first episode psychosis, but suggest that some treatment-related changes in mI might be apparent in patients with schizophrenia-spectrum diagnoses. Seemingly illness-related Cr/PCr elevations were also specific to the diagnosis of schizophrenia-spectrum disorder and seem worthy of future study.

Strategic short termism as an issue of top-teams’ temporal orientation

Short-termism among firms, the tendency to excessively discount long-term benefits and favour less valuable short-term benefits, has been a prominent issue in business and public policy debates but research to date has been inconclusive. We study how managers frame, interpret, and resolve problems of intertemporal choice in actual decisions by using computer aided text analysis to measure the frequency of top-team temporal references in 1653 listed Australian firms between 1992-2005. Contrary to short-termism arguments we find evidence of a significant general increase in Future orientation and a significant decrease in Current/Past orientation. We also show top-teams’ temporal orientation is related to their strategic orientation, specifically the extent to which they focus on Innovation-Expansion and Capacity Building.

Functional outcome of transfemoral amputees fitted with an osseointegrated fixation : temporal gait characteristics

The purpose of this study was to characterise the functional outcome of 12 transfemoral amputees fitted with osseointegrated fixation using temporal gait characteristics. The objectives were (A) to present the cadence, duration of gait cycle, support and swing phases with an emphasis on the stride-to-stride and participant-to-participant variability, and (B) to compare these temporal variables with normative data extracted from the literature focusing on transfemoral amputees fitted with a socket and able-bodied participants. The temporal variables were extracted from the load applied on the residuum during straight level walking, which was collected at 200 Hz by a transducer. A total of 613 strides were assessed. The cadence (46±4 strides/min), the duration of the gait cycle (1.29±0.11 s), support (0.73±0.07 s, 57±3% of CG) and swing (0.56±0.07 s, 43±3% of GC) phases of the participants were 2% quicker, 3%, 6% shorter and 1% longer than transfemoral amputees using a socket as well as 11% slower, 9%, 6% and 13% longer than able-bodied, respectively. All combined, the results indicated that the fitting of an osseointegrated fixation has enabled this group of amputees to restore their locomotion with a highly functional level. Further longitudinal and cross-sectional studies would be required to confirm these outcomes. Nonetheless, the data presented can be used as benchmark for future comparisons. It can also be used as input in generic algorithms using templates of patterns of loading to recognise activities of daily living and to detect falls.