Probabilities on Sentences in an Expressive Logic

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.Comment: 52 LaTeX pages, 64 definiton/theorems/etc, presented at conference Progic 2011 in New Yor

Surgical therapy for atrial tachycardia in adults

AbstractEighteen adult patients with atrial tachycardia refractory to treatment with a mean of four drugs underwent attempted surgical cure. Atrial tachycardia originated in the right atrium in 17 patients and the left atrium in 1 patient. Tachycardia could be reproducibly induced and terminated by atrial extrastimuli or atrial pacing in 8 patients (44%). Resection of the arrhythmogenic area was performed in 16 patients (89%), and an isolation procedure was performed in 1 patient. In seven cases (39%), the area of isolation or excision included the sinoatrial node. One patient underwent His bundle section because the arrhythmogenic region was too close to the atrioventricular (AV) conduction system to enable resection.The mean duration of clinical follow-up was 56 ± 34 months. Clinical tachycardia recurred in five patients (28%), but in two patients it did not recur until >1 year after surgery. A permanent pacemaker was implanted in 3 (18%) of the 17 patients whose His-Purkinje system was left intact. One other patient had required permanent pacing before surgery. Only one of the seven patients undergoing sinoatrial node resection or isolation required permanent pacing for symptomatic bradycardia. Apart from the requirement for permanent pacing, no significant complications occurred.Surgical therapy for atrialtachycardia is a safe procedure, but the rate of cure appears to be less than that of supraventricular tachycardias associated with accessory AV connections. Excision or isolation of the sinoatrial node does not necessitate permanent pacing in most patients

Surgical procedure for the cure of atrioventricular junctional (“AV node”) reentrant tachycardia: Anatomic and electrophysiologic effects of dissection of the anterior atrionodal connections in a canine model

AbstractObjectives. This study was undertaken to examine the electrophysiologic and anatomic efects of a surgical procedure that cures the anterior (common) type of atrioventricular (AV) junciional reentrant tachycardia.Background. The procedure was designed to interrupt the reentrant circuit at the point of earliest atrial activation during AV junctional reentrant tachycardia, the anterior atrionodal connections.Methods. Atrioventricular node function and the sequence of electrical excitation of Koch's triangle were examined in 18 dogs. Excitation of Koch's triangle was mapped using a 60-channel mapping system. Surgical dissection was performed in 10 dogs and a sham procedure in 8. After 28 to 35 days, AV node function and the atrial excitation pattern were reassessed. The AV junction was examined using light microscopy.Results. Some degree of AV node damage was visible in all dogs in the dissection group, but it was minor in 40% of cases. The anterior part of the AV node was disconnected from the anterior atrionodal connections in all cases. Anterograde AV node function was mildly impaired. The median AH interval was increased (62 vs. 76 ms [interquartile ranges 48 to 72 and 64 to 104, respectively], P = 0.05), and the AV Wenckebach cycle length was increased (210 vs. 245 ms [interquartile ranges 200 to 230 and 210 to 260, respectively], p = 0.02). The degree of impairment of conduction was directly proportional to the length of dissection (p < 0.05) but not to the degree of damage to the AV node. Ventriculoatrial (VA) conduction was destroyed in 50% of dogs undergoing dissection but in none of those with a sham operation (p < 0.04). The AV node remained responsive to autonomic blocking drugs, and atrial mapping during ventricular pacing revealed that the site of exit from the AV node had been altered.Conclusions. The atrionodal connections closest to the His bundle are the preferred route of conduction through the AV node during normal AV or VA conduction. Destruction of these connections modifies AV node conduction. The surgical procedure selectively interrupts these connections, and this interruption is likely to be the mechanism of cure

Differences between patients with ventricular tachycardia and ventricular fibrillation as assessed by signal-averaged electrocardiogram, radionuclide ventriculography and cardiac mapping

AbstractThis study examined 65 patients with ventricular tachycardia or fibrillation late after myocardial infarction to determine whether they differed with respect to duration of ventricular activation in sinus rhythm and left ventricular ejection fraction. Patients with spontaneous ventricular tachycardia had a longer ventricular activation time in sinus rhythm than did patients with spontaneous ventricular fibrillation. This difference was detected with the signal-averaged electrocardiogram (ECG) (tachycardia 181 ± 33 ms, fibrillation 152 ± 23 ms, p < 0.001) and at epicardial mapping (tachycardia 210 ± 17 ms, fibrillation 192 ± 17 ms, p < 0.02). Left ventricular ejection fraction was lower in patients with spontaneous ventricular tachycardia (0.22 ± 0.09) than in patients with spontaneous ventricular fibrillation (0.27 ± 0.09) (p < 0.05).The patients with both spontaneous and inducible ventricular fibrillation had a shorter ventricular activation time on the signal-averaged ECG (129 ± 17 ms) and a higher ejection fraction (0.36 ± 0.05) than did either patients with spontaneous ventricular fibrillation and inducible ventricular tachycardia (158 ± 21 ms and 0.25 ± 0.08, respectively, each p < 0.01) or patients with both spontaneous and inducible ventricular tachycardia (181 ± 33 ms and 0.22 ± 0.09, respectively, each p < 0.001). Of the patients with inducible ventricular tachycardia, presentation with tachycardia rather than fibrillation was associated with a longer ventricular activation time on the signal-averaged ECG (181 ± 33 versus 158 ± 21 ms, p < 0.02) and a longer cycle length of inducible ventricular tachycardia (290 ± 61 versus 259 ± 44 ms, p = 0.05).In conclusion, conduction delay during sinus rhythm and left ventricular dysfunction appear to be greatest in patients with spontaneous and inducible ventricular tachycardia, and least in patients with spontaneous and inducible ventricular fibrillation

Electrophysiologic and histologic effects of dissection of the connections between the atrium and posterior part of the atrioventricular node

AbstractObjectives. This study was designed to examine the effects of destroying the posterior approaches to the atrioventricular (AV) node.Background. Surgical and catheter ablation procedures have been developed for the cure of AV junctional reentrant tachycardia. Some of these destroy the posterior approaches to the AV node.Methods. Atrioventricular node function and electrical excitation of Koch's triangle and the proximal coronary sinus were examined in 18 dogs. Dissection of the posterior atrionodal connections was performed in 10 dogs and a sham procedure in 8. After 28 to 35 days, repeat electrophysiologic and mapping studies were performed to assess changes in AV node function and the routes of AV and ventriculoatrial (VA) conduction. The AV junction was then examined with light microscopy.Results. The compact AV node was undamaged in eight cases (80%). In two cases minor fibrosis occurred at the posterior limit of the compact node. The right-sided posterior atrionodal connections lying between the coronary sinus orifice and the tricuspid annulus were replaced by scar tissue in all cases, but the left-sided posterior connections and the anterior connections remained intact. Atrioventricular and VA conduction intervals and refractory periods were not altered. Atrioventricular junctional echoes were present in 10 dogs before and in 7 dogs after dissection (p = 0.06). Posterior (slow pathway) retrograde exits from the AV node were present in seven dogs before and in seven dogs after dissection. However, retrograde atrial excitation was altered in four of these seven dogs, so that the site of exit from the AV node was more leftward than it had been preoperatively. The node remained responsive to autonomic blocking drugs postoperatively. Double atrial electrograms similar to slow pathway potentials were found in all dogs.Conclusions. This procedure ablates the posterior atrionodal connections but rarely damages the compact AV node. Atrioventricular node function is not impaired and the node is not denervated. The mechanism of cure of AV junctional reentrant tachycardia is probably damage to the perinodal atrium. This suggests that part of the slow AV node pathway may lie outside the compact AV node. Dual AV node exits and double atrial electrograms are present in the normal canine heart