Programming in Logic Without Logic Programming
... empty conjunction of FOL conditions and temporal constraints. All time variables in temporal constraints in the complex occur as time parameters in FOL conditions of the complex or are functionally dependent on such time parameters. For example, T3 is functionally dependent on T1 and T2 in max(T1, T ...
... empty conjunction of FOL conditions and temporal constraints. All time variables in temporal constraints in the complex occur as time parameters in FOL conditions of the complex or are functionally dependent on such time parameters. For example, T3 is functionally dependent on T1 and T2 in max(T1, T ...
On modal logics of group belief
... of ‘a decision to treat p as true in one’s utterances and actions’ without being necessarily (see [61] for instance) connected to the actual truth of the proposition. In the present article, the notion of acceptance qua member of an institution is also applied to the collective level named collectiv ...
... of ‘a decision to treat p as true in one’s utterances and actions’ without being necessarily (see [61] for instance) connected to the actual truth of the proposition. In the present article, the notion of acceptance qua member of an institution is also applied to the collective level named collectiv ...
Plausibility structures for default reasoning
... shown it to encompass various kinds of default reasoning [4, 5]. A feature of this inference is that the rule (AND) – if ψ1 and ψ2 can be derived, then their conjunction ψ1 ∧ ψ2 can be derived – is not necessarily satisfied. Many interesting cases where the rule (AND) should not be satisfied are kno ...
... shown it to encompass various kinds of default reasoning [4, 5]. A feature of this inference is that the rule (AND) – if ψ1 and ψ2 can be derived, then their conjunction ψ1 ∧ ψ2 can be derived – is not necessarily satisfied. Many interesting cases where the rule (AND) should not be satisfied are kno ...
x - Homepages | The University of Aberdeen
... II. Construct a model where 1 and 4 are true, while 2 and 3 are false 1. x (Q(x) P(x)) (true for place a below) 2. x (Q(x) P(x)) (false for places b below) 3. x (Q(x) P(x)) (false for place b below) 4. x (Q(x) P(x)) (true for place a below) One solution: a model with exactly two objects i ...
... II. Construct a model where 1 and 4 are true, while 2 and 3 are false 1. x (Q(x) P(x)) (true for place a below) 2. x (Q(x) P(x)) (false for places b below) 3. x (Q(x) P(x)) (false for place b below) 4. x (Q(x) P(x)) (true for place a below) One solution: a model with exactly two objects i ...
1 Non-deterministic Phase Semantics and the Undecidability of
... argument and compare this proof with Okada’s one. In Section 5, we prove the undecidability of validity in eILL. We describe first informally then formally how to encode the computation steps of Minsky machines using the rules of G-eILL. The completeness of the encoding is obtained by a simple seman ...
... argument and compare this proof with Okada’s one. In Section 5, we prove the undecidability of validity in eILL. We describe first informally then formally how to encode the computation steps of Minsky machines using the rules of G-eILL. The completeness of the encoding is obtained by a simple seman ...
Harmony, Normality and Stability
... Dummett singles out two features of the use of expressions that are of central importance for specifying their meanings. The two features are intended to apply very generally to all kinds of expressions, but I’m only concerned with the logical constants. ‘The first category [of principles governing ...
... Dummett singles out two features of the use of expressions that are of central importance for specifying their meanings. The two features are intended to apply very generally to all kinds of expressions, but I’m only concerned with the logical constants. ‘The first category [of principles governing ...
Proof theory for modal logic
... for introducing the universal quantifier. For a survey on the debate around the deduction theorem in modal logic, see Hakli and Negri (2011). ...
... for introducing the universal quantifier. For a survey on the debate around the deduction theorem in modal logic, see Hakli and Negri (2011). ...
Notes on the Science of Logic
... but instead we shall try to keep track of the principles involved. Principles, however, come at many levels, so we must be more specific. In contrast to much of mathematical logic, proofs in these notes will use what most logicians consider only the most elementary of steps. In fact, this presentati ...
... but instead we shall try to keep track of the principles involved. Principles, however, come at many levels, so we must be more specific. In contrast to much of mathematical logic, proofs in these notes will use what most logicians consider only the most elementary of steps. In fact, this presentati ...
Ethical Intuitionism: The Meaning of Meaning Senior
... action can be good but only in the sense of satisfying physical or psychological properties whereas the eliminativists deny that an action can be good at all. However, both reductionists and eliminativists reject the existence of any set of moral properties beyond natural ones. In this sense, ethica ...
... action can be good but only in the sense of satisfying physical or psychological properties whereas the eliminativists deny that an action can be good at all. However, both reductionists and eliminativists reject the existence of any set of moral properties beyond natural ones. In this sense, ethica ...
Interpreting and Applying Proof Theories for Modal Logic
... vocabulary is governed by its own introduction and elimination rules, in which each of those rules is separable, so we can specify the rules for one concept independently of the rules for an of the others, and in which proofs can be composed, manipulated and transformed in natural ways, then the sit ...
... vocabulary is governed by its own introduction and elimination rules, in which each of those rules is separable, so we can specify the rules for one concept independently of the rules for an of the others, and in which proofs can be composed, manipulated and transformed in natural ways, then the sit ...
Sample pages 2 PDF
... We have just defined what a formulae in propositional calculus should look like. We have also seen how such formulae correspond to English sentences, which can be either true or false. The next step is to build a series of mathematical tools to reason about these formulae. For instance, some stateme ...
... We have just defined what a formulae in propositional calculus should look like. We have also seen how such formulae correspond to English sentences, which can be either true or false. The next step is to build a series of mathematical tools to reason about these formulae. For instance, some stateme ...
a PDF file of the textbook - U of L Class Index
... The first of these deductions is very famous, but the second one is lame. It may seem odd to even call it a deduction, because the two hypotheses have nothing at all to do with the conclusion, but, given our definition, it does count as a deduction. However, it is is a very poor one, so it cannot be ...
... The first of these deductions is very famous, but the second one is lame. It may seem odd to even call it a deduction, because the two hypotheses have nothing at all to do with the conclusion, but, given our definition, it does count as a deduction. However, it is is a very poor one, so it cannot be ...
On the meanings of the logical constants and the justifications of the
... and Frege. And, through Frege’s influence, the whole of modern logic has come to be based on the single form of judgement, or assertion, A is true. Once this step was taken, the question arose, What sort of thing is it that is affirmed in an affirmation and denied in a denial? that is, What sort of ...
... and Frege. And, through Frege’s influence, the whole of modern logic has come to be based on the single form of judgement, or assertion, A is true. Once this step was taken, the question arose, What sort of thing is it that is affirmed in an affirmation and denied in a denial? that is, What sort of ...
On the Meaning of the Logical Constants and the
... has come to be based on the single form of judgement, or assertion, A is true. Once this step was taken, the question arose, What sort of thing is it that is affirmed in an affirmation and denied in a denial? that is, What sort of thing is the A here? The isolation of this concept belongs to the, if ...
... has come to be based on the single form of judgement, or assertion, A is true. Once this step was taken, the question arose, What sort of thing is it that is affirmed in an affirmation and denied in a denial? that is, What sort of thing is the A here? The isolation of this concept belongs to the, if ...
Proofs in Propositional Logic
... In Coq, the negation of a proposition A is represented with the help of a constant not, where not A (also written ∼A) is defined as the implication A→False. The tactic unfold not allows to expand the constant not in a goal, but is seldom used. The introduction tactic for ∼A is the introduction tactic ...
... In Coq, the negation of a proposition A is represented with the help of a constant not, where not A (also written ∼A) is defined as the implication A→False. The tactic unfold not allows to expand the constant not in a goal, but is seldom used. The introduction tactic for ∼A is the introduction tactic ...
Proofs in Propositional Logic
... In Coq, the negation of a proposition A is represented with the help of a constant not, where not A (also written ∼A) is defined as the implication A→False. The tactic unfold not allows to expand the constant not in a goal, but is seldom used. The introduction tactic for ∼A is the introduction tactic ...
... In Coq, the negation of a proposition A is represented with the help of a constant not, where not A (also written ∼A) is defined as the implication A→False. The tactic unfold not allows to expand the constant not in a goal, but is seldom used. The introduction tactic for ∼A is the introduction tactic ...
ppt - UBC Computer Science
... To prove this statement is true, we must Find a value of x (a “witness”) for which P(x) holds. ...
... To prove this statement is true, we must Find a value of x (a “witness”) for which P(x) holds. ...
article in press - School of Computer Science
... monadic two-variable guarded fragment GF 2mon of classical first-order logic, where guard relations satisfy conditions that can be expressed as monadic second-order definable closure constraints, is decidable. Our contribution is a slight generalisation of this result to account for conditions which ...
... monadic two-variable guarded fragment GF 2mon of classical first-order logic, where guard relations satisfy conditions that can be expressed as monadic second-order definable closure constraints, is decidable. Our contribution is a slight generalisation of this result to account for conditions which ...
Lecture Slides
... To prove this statement is true, we must Find a value of x (a “witness”) for which P(x) holds. ...
... To prove this statement is true, we must Find a value of x (a “witness”) for which P(x) holds. ...
Towards an Epistemic Logic of Grounded Belief
... in the model M she is reasoning within. For the most part, logicians and computer-scientists like to hold that ideal knowers know at least all local validities (Halpern, 1999; Hintikka, 1962; Lenzen, 1978; Meyer and van der Hoek, 1995). Minimally, if an ideal knower only knew (φ → (ψ → φ)), ((φ → ( ...
... in the model M she is reasoning within. For the most part, logicians and computer-scientists like to hold that ideal knowers know at least all local validities (Halpern, 1999; Hintikka, 1962; Lenzen, 1978; Meyer and van der Hoek, 1995). Minimally, if an ideal knower only knew (φ → (ψ → φ)), ((φ → ( ...
A System of Interaction and Structure
... deep reasons for this kind of logic not to be expressible in the sequent calculus, and there is a simple formalism, which we call the calculus of structures, that is instead able to express self-dual non-commutativity with great ease. In fact, self-dual non-commutative operators naturally generate a ...
... deep reasons for this kind of logic not to be expressible in the sequent calculus, and there is a simple formalism, which we call the calculus of structures, that is instead able to express self-dual non-commutativity with great ease. In fact, self-dual non-commutative operators naturally generate a ...
On two problems with the Theory of the Creating Subject
... quences, in which case, to my mind, it is highly plausible. First note that on the Brouwerian conception of logic, p → q means ‘Whenever a construction for p has been effected, it can be continued into a construction for q’. That a construction for p has been effected may of course be wholly hypoth ...
... quences, in which case, to my mind, it is highly plausible. First note that on the Brouwerian conception of logic, p → q means ‘Whenever a construction for p has been effected, it can be continued into a construction for q’. That a construction for p has been effected may of course be wholly hypoth ...
Fichte`s Legacy in Logic
... combination of representations; hence the very possibility of judgment depends on the availability of at least two representations that can be combined. Since the general logic of judgment deals only with general representations (i.e., not with intuitions), any judgment that is recognized in logic ...
... combination of representations; hence the very possibility of judgment depends on the availability of at least two representations that can be combined. Since the general logic of judgment deals only with general representations (i.e., not with intuitions), any judgment that is recognized in logic ...
The Foundations
... sentence referred to. =>Example: Since it is not raining now(the current situation), the statement It_is_raining is false (in the current situation). But if it were raining now, then I would say that It_is_raining is true. Factors affecting the truth value of a proposition: the situation in whic ...
... sentence referred to. =>Example: Since it is not raining now(the current situation), the statement It_is_raining is false (in the current situation). But if it were raining now, then I would say that It_is_raining is true. Factors affecting the truth value of a proposition: the situation in whic ...